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Tag
roots
Recent questions tagged roots
65
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1
answers
Determine the value(s) of \(m\) for which the equation \(m x^2-12 x+9=0\) has equal roots.
Given: \(\quad X=\sqrt{e-4}\)Write down the value of \(e\), for which \(X\) is:1. Zero2. Non-realDetermine the value(s) of \(m\) for which the equation \(m x^2-12 x+9=0\)...
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Mathematics
zero
non-real
roots
equation
+
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130
views
2
answers
Find the point(s) on the parabola \( 2 x=y^{2} \) closest to the point \( (1,0) \).
Find the point(s) on the parabola \( 2 x=y^{2} \) closest to the point \( (1,0) \).
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Feb 7
Mathematics
fraction
fractions
raphson
method
roots
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170
views
1
answers
Given the equation \(4(x+1)=3x+10\). For which values of \(x\) is the equation true?
Given the equation \(4(x+1)=3x+10\). For which values of \(x\) is the equation true?
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113k
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Jan 9
Mathematics
equation
roots
solution
positive
inverse
non-real
matrices
+
–
224
views
1
answers
For which values of \(k\) will the equation \(x^2+6 x-2 k=0\) have non-real roots?
For which values of \(k\) will the equation \(x^2+6 x-2 k=0\) have non-real roots?
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113k
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Oct 19, 2023
Mathematics
equation
roots
non-real
positive
solution
matrices
inverse
+
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666
views
1
answers
Calculate the roots of the cubic equation \(x^3-8=0\), show all working.
Calculate the roots of the cubic equation \(x^3-8=0\), show all working. Use latex.
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Platinum
113k
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Mar 29, 2023
Mathematics
equation
graph
cubic
polynomial
coefficients
solve
roots
+
–
318
views
1
answers
Give an example of how to find the roots of a complex number.
Give an example of how to find the roots of a complex number. use latex
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113k
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Mar 29, 2023
Mathematics
example
roots
complex
number
+
–
206
views
0
answers
For which value(s) of will the equation 2( + 1) + = have equal roots?
Using quadratic equations
abbyrigby06
103
points
abbyrigby06
asked
Feb 3, 2023
Mathematics
roots
equation
quadratic
+
–
467
views
1
answers
Without solving for \(x\), determine the nature of the roots of the following equation: \[ x^2-4 x=-3 \]
Without solving for \(x\), determine the nature of the roots of the following equation:\[x^2-4 x=-3\]
AstraNova
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68.1k
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AstraNova
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Jan 30, 2023
Mathematics
equation
roots
function
nature
calculation
plane
line
+
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508
views
1
answers
Given that \(2 x^2+(p-3) x+8=0\), determine the value(s) of \(p\) for which the roots will be non-real.
Given that \(2 x^2+(p-3) x+8=0\), determine the value(s) of \(p\) for which the roots will be non-real.
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68.1k
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Jan 30, 2023
Mathematics
roots
equation
non-real
positive
solution
matrices
inverse
+
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381
views
1
answers
The roots of a quadratic equation are given as \(x=\dfrac{-2 \pm \sqrt{1-3 k}}{4}\).
The roots of a quadratic equation are given as \(x=\dfrac{-2 \pm \sqrt{1-3 k}}{4}\).a) For which value(s) of \(k\) will the roots be real?b) For which value(s) of \(k\) w...
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68.1k
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Jan 30, 2023
Mathematics
roots
equation
calculate
real
theorem
calculus
circle
+
–
529
views
0
answers
If \(a^2(c-b) ; a(c-b) ; b-a\) forms a geometric sequence, prove that \(a ; b ; c\) forms an arithmetic sequence.
If \(a^2(c-b) ; a(c-b) ; b-a\) forms a geometric sequence, prove that \(a ; b ; c\) forms an arithmetic sequence.
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113k
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Jan 21, 2023
Mathematics
prove
lines
convex
quadrilateral
angles
equation
roots
+
–
411
views
0
answers
If \(a x^2+2 b x+c=0\) has equal roots, prove that \(a ; b ; c\) forms a geometric sequence.
If \(a x^2+2 b x+c=0\) has equal roots, prove that \(a ; b ; c\) forms a geometric sequence.
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113k
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Jan 21, 2023
Mathematics
prove
convex
lines
quadrilateral
angles
equation
roots
+
–
202
views
0
answers
The roots of the polynomial \(x^4-4 i x^3+3 x^2-14 i x-44\) form the vertices of a parallelogram in the complex plane. What is the area of the parallelogram?
The roots of the polynomial \(x^4-4 i x^3+3 x^2-14 i x-44\) form the vertices of a parallelogram in the complex plane. What is the area of the parallelogram?
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113k
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Dec 8, 2022
Mathematics
roots
polynomial
vertices
complex
plane
+
–
359
views
0
answers
Let \(r, s, t\) be the roots of the equation \(x(x-2)(3 x-7)=2\). Show that \(r, s, t\) are real and positive and determine \(\arctan r+\arctan s+\arctan t\).
Let \(r, s, t\) be the roots of the equation \(x(x-2)(3 x-7)=2\). Show that \(r, s, t\) are real and positive and determine \(\arctan r+\arctan s+\arctan t\).
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113k
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Sep 23, 2022
Mathematics
equation
positive
solution
inverse
matrices
roots
distinct
+
–
240
views
0
answers
Find the roots \(r_1, r_2, r_3, r_4\) of the equation \(4 x^4-a x^3+b x^2-c x+5=0\), assuming that they are positive real numbers and that
Find the roots \(r_1, r_2, r_3, r_4\) of the equation \(4 x^4-a x^3+b x^2-c x+5=0\), assuming that they are positive real numbers and that\[\frac{r_1}{2}+\frac{r_2}{4}+\f...
MathsGee
Platinum
113k
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MathsGee
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Sep 23, 2022
Mathematics
equation
roots
matrices
distinct
solution
inverse
positive
+
–
274
views
0
answers
Find the number of real roots of the equation ...
Find the number of real roots of the equation\[x^8-x^7+2 x^6-2 x^5+3 x^4-3 x^3+4 x^2-4 x+\frac{5}{2}=0 .\]
MathsGee
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113k
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Sep 23, 2022
Mathematics
roots
equation
solution
distinct
matrices
inverse
real
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286
views
0
answers
Find the number of real roots of the equation
Find the number of real roots of the equation\[x^8-x^7+2 x^6-2 x^5+3 x^4-3 x^3+4 x^2-4 x+\frac{5}{2}=0 .\]
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113k
points
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Sep 22, 2022
Mathematics
equation
roots
real
calculate
logarithms
circle
theorem
+
–
513
views
0
answers
Find the roots of the equation \[ z^2+2 z+17=0, \]
(a) Find the roots of the equation\[z^2+2 z+17=0,\]giving your answers in the form \(a+\mathrm{i} b\), where \(a\) and \(b\) are integers.(b) Show these roots on an Argan...
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113k
points
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asked
Sep 13, 2022
Mathematics
complex
equation
solution
numbers
real
jee
roots
+
–
211
views
1
answers
Write down the value of the real root of the equation \[ x^3-64=0 \]
(a) Write down the value of the real root of the equation\[x^3-64=0\](b) Find the complex roots of \(x^3-64=0\), giving your answers in the form \(a+\mathrm{i} b\), where...
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113k
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Sep 13, 2022
Mathematics
equation
calculus
real
derivative
function
numbers
roots
+
–
277
views
1
answers
\[ f(x)=x^3+x^2+44 x+150 \] Given that \(\mathrm{f}(x)=(x+3)\left(x^2+a x+b\right)\), where \(a\) and \(b\) are real constants,
\[f(x)=x^3+x^2+44 x+150\]Given that \(\mathrm{f}(x)=(x+3)\left(x^2+a x+b\right)\), where \(a\) and \(b\) are real constants,(a) find the value of \(a\) and the value of \...
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113k
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Sep 13, 2022
Mathematics
roots
real
imaginary
complex
number
+
–
267
views
0
answers
How do I determine squares, square roots, cubes and cube roots of algebraic terms?
How do I determine squares, square roots, cubes and cube roots of algebraic terms?
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113k
points
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Sep 7, 2022
Mathematics
squares
square
roots
cubes
cube
algebraic
terms
+
–
346
views
1
answers
Can i determine the nature of roots of an equation or function without doing the calculation?
Can i determine the nature of roots of an equation or function without doing the calculation?
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113k
points
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asked
Sep 7, 2022
Mathematics
nature
roots
equation
function
calculation
+
–
362
views
0
answers
The number of distinct terms in \((a+b+c+d+e)^{4}\) is
The number of distinct terms in \((a+b+c+d+e)^{4}\) is
AstraNova
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68.1k
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AstraNova
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Aug 15, 2022
Mathematics
distinct
matrices
equation
solution
inverse
roots
numbers
+
–
621
views
1
answers
\[ x^{2}+2 x+3=0 \] if a is one of its roots, then \[ \frac{a^{5}+3 a^{4}+3 a^{3}-a^{2}}{a^{2}+3}=? \]
\[x^{2}+2 x+3=0\]if a is one of its roots, then\[\frac{a^{5}+3 a^{4}+3 a^{3}-a^{2}}{a^{2}+3}=?\]
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68.1k
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Jul 22, 2022
Mathematics
numbers
jee
real
integers
complex
set
roots
+
–
229
views
1
answers
Find the unique value of \(a\) for which the polynomial \(x^{3}-12 x^{2}+a x-64\) has all real, nonnegative roots.
Find the unique value of \(a\) for which the polynomial \(x^{3}-12 x^{2}+a x-64\) has all real, nonnegative roots.
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Platinum
113k
points
MathsGee
asked
Jul 7, 2022
Mathematics
real
numbers
roots
equation
function
calculus
derivative
+
–
253
views
1
answers
Find all the integer roots of \(2 x^{4}+4 x^{3}-5 x^{2}+2 x-3=0\). Enter all the integer roots, separated by commas.
Find all the integer roots of \(2 x^{4}+4 x^{3}-5 x^{2}+2 x-3=0\). Enter all the integer roots, separated by commas.
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Platinum
113k
points
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asked
Jul 7, 2022
Mathematics
roots
solution
matrices
distinct
numbers
+
–
271
views
1
answers
Find all the integer roots of \[ x^{4}+5 x^{3}+9 x^{2}-x-14=0 . \] Enter all the integer roots, separated by commas.
Find all the integer roots of\[x^{4}+5 x^{3}+9 x^{2}-x-14=0 .\]Enter all the integer roots, separated by commas.
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113k
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asked
Jul 7, 2022
Mathematics
equation
roots
solution
matrices
inverse
distinct
numbers
+
–
502
views
1
answers
Let \(a, b, c, d\), and \(e\) be the distinct roots of the equation \(x^{5}+7 x^{4}-2=0\). Find
Let \(a, b, c, d\), and \(e\) be the distinct roots of the equation \(x^{5}+7 x^{4}-2=0\). Find\[\begin{aligned}&\frac{a^{3}}{(a-b)(a-c)(a-d)(a-e)}+\frac{b^{3}}{(b-a)(b-c...
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113k
points
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asked
Jul 7, 2022
Mathematics
distinct
roots
equation
solution
inverse
matrices
+
–
317
views
1
answers
For how many different values of \(x\) does \(x^{5}=x^{4}+72 x^{3}\) ?
For how many different values of \(x\) does \(x^{5}=x^{4}+72 x^{3}\) ?
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113k
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asked
Jul 7, 2022
Mathematics
equation
combinations
calculate
solve
real
roots
permutations
+
–
355
views
1
answers
If \[ C_{0}+\frac{C_{1}}{2}+\cdots+\frac{C_{n-1}}{n}+\frac{C_{n}}{n+1}=0 \] where \(C_{0}, \ldots, C_{n}\) are real constants, prove that the equation
If\[C_{0}+\frac{C_{1}}{2}+\cdots+\frac{C_{n-1}}{n}+\frac{C_{n}}{n+1}=0\]where \(C_{0}, \ldots, C_{n}\) are real constants, prove that the equation\[C_{0}+C_{1} x+\cdots+C...
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68.1k
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Jul 5, 2022
Mathematics
real
constants
roots
integers
expression
function
equation
+
–
262
views
1
answers
Prove that \(\sum 1 / p\) diverges; the sum extends over all primes.
Prove that \(\sum 1 / p\) diverges; the sum extends over all primes.(This shows that the primes form a fairly substantial subset of the positive integers.)Hint: Given \(N...
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Diamond
68.1k
points
AstraNova
asked
Jul 5, 2022
Mathematics
real
equation
roots
quadratic
rational
non-real
prove
+
–
178
views
1
answers
Solve \(5x^2-49=0 \)
Solve \(5x^2-49=0 \)
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113k
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asked
Jun 22, 2022
Mathematics
equation
solve
solution
linear
roots
equations
function
+
–
428
views
1
answers
If \({ }^{n} P_{r}:^{n} C_{r}=120\) then find \(n\) and \(r\)
If \({ }^{n} P_{r}:^{n} C_{r}=120\) then find \(n\) and \(r\)
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113k
points
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asked
Jun 22, 2022
Mathematics
real
constants
roots
expression
integers
sequence
analysis
+
–
427
views
1
answers
Show that \(x^{2}+2 x^{2}+5=0\) has non-real roots
Show that \(x^{2}+2 x^{2}+5=0\) has non-real roots
Junior
104
points
Junior
asked
May 15, 2022
General Knowledge
non-real
roots
quadratic
+
–
288
views
0
answers
\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integers
\(\mathrm{a}, \mathrm{b}, \ldots, \mathrm{e}\) are positive integersabcde \(=a+b+c+d+e\)\(\max (\max (a, b, c, d, e))=?\)
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68.1k
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May 5, 2022
Mathematics
integers
real
roots
expression
constants
positive
numbers
+
–
624
views
0
answers
For what values of the constant \(c\) does \(\ln x=c x^{2}\) have solutions. Assume that \(c>0\).
For what values of the constant \(c\) does \(\ln x=c x^{2}\) have solutions. Assume that \(c>0\).
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68.1k
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Feb 4, 2022
Mathematics
equation
roots
npv
project
wacc
cashflow
irr
+
–
564
views
0
answers
Find a curve \(y=f(x)\) with the following properties:
Find a curve \(y=f(x)\) with the following properties:- \(\frac{d^{2} y}{d x^{2}}=6 x\)- Its graph passes through the point \((0,1)\) and has a horizontal tangent there.
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68.1k
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Feb 4, 2022
Mathematics
newton
raphson
method
solutions
roots
fraction
fractions
+
–
940
views
1
answers
Find, correct to 5 decimal places, the \(x\)-coordinate of the point on the curve \(y=\ln x\) which is closest to the origin. Use the Newton Method.
Find, correct to 5 decimal places, the \(x\)-coordinate of the point on the curve \(y=\ln x\) which is closest to the origin. Use the Newton Method.
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113k
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asked
Feb 1, 2022
Mathematics
newton
raphson
solutions
roots
method
fraction
fractions
+
–
1.6k
views
1
answers
Use the Newton Method to find the smallest and the second smallest positive roots of the equation \(\tan x=4 x\), correct to 4 decimal places.
Use the Newton Method to find the smallest and the second smallest positive roots of the equation \(\tan x=4 x\), correct to 4 decimal places.
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113k
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asked
Feb 1, 2022
Mathematics
newton
raphson
solutions
roots
fraction
fractions
method
+
–
1.3k
views
1
answers
A calculator is defective: it can only add, subtract, and multiply. Use the equation \(1 / x=1.37\), the Newton Method, and the defective calculator to find \(1 / 1.37\) correct to 8 decimal places.
A calculator is defective: it can only add, subtract, and multiply. Use the equation \(1 / x=1.37\), the Newton Method, and the defective calculator to find \(1 / 1.37\) ...
MathsGee
Platinum
113k
points
MathsGee
asked
Feb 1, 2022
Mathematics
newton
raphson
solutions
roots
fraction
fractions
+
–
1.3k
views
1
answers
Find all solutions of \(5 x+\ln x=10000\), correct to 4 decimal places; use the Newton Method.
Find all solutions of \(5 x+\ln x=10000\), correct to 4 decimal places; use the Newton Method.
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Platinum
113k
points
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asked
Feb 1, 2022
Mathematics
method
solutions
newton
raphson
roots
fractions
fraction
+
–
1.5k
views
1
answers
Find all solutions of \(e^{2 x}=x+6\), correct to 4 decimal places; use the Newton Method.
Find all solutions of \(e^{2 x}=x+6\), correct to 4 decimal places; use the Newton Method.
MathsGee
Platinum
113k
points
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asked
Feb 1, 2022
Mathematics
newton
raphson
solutions
roots
method
+
–
259
views
1
answers
Solve the equation: \(5(2-3x)+3(5x-2)-7(4-x)=0\)
Solve the equation:\(5(2-3x)+3(5x-2)-7(4-x)=0\)
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Platinum
113k
points
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asked
Jan 13, 2022
Mathematics
solve
equation
linear
solution
roots
+
–
517
views
1
answers
Solve the proportion \(\dfrac{5}{3}=\dfrac{x}{6}\) for the unknown value \(x\).
Solve the proportion \(\dfrac{5}{3}=\dfrac{x}{6}\) for the unknown value \(x\).
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Platinum
113k
points
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asked
Jan 3, 2022
Mathematics
calculus
solve
calculate
equation
real
quadratic
roots
+
–
353
views
1
answers
Prove that, for all values of \(x\), \[ x^{2}+4 x+12>x+3 \]
Prove that, for all values of \(x\),\[x^{2}+4 x+12>x+3\]
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Platinum
113k
points
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asked
Nov 9, 2021
Mathematics
roots
nature
inequality
discriminant
prove
grade12
+
–
662
views
1
answers
Show that \(x^{2}-6 x+11>0\) for all real values of \(x\).
Show that \(x^{2}-6 x+11>0\) for all real values of \(x\).
MathsGee
Platinum
113k
points
MathsGee
asked
Nov 9, 2021
Mathematics
equation
roots
real
non-real
quadratic
numbers
integers
+
–
437
views
1
answers
If \(x^{2}-k x+9=0\) has equal roots, find the values of \(k\).
If \(x^{2}-k x+9=0\) has equal roots, find the values of \(k\).A. 3,4B. \(\pm 3\)C. \(\pm 5\)D. \(\pm 6\)
Siyavula
Wooden Status
4.3k
points
Siyavula
asked
Sep 11, 2021
Mathematics
roots
parabola
functions
values
equation
calculate
real
+
–
410
views
1
answers
What is the prime factorization of 136?
What is the prime factorization of 136?
MathsGee
Platinum
113k
points
MathsGee
asked
Sep 10, 2021
Mathematics
numbers
calculate
factorization
prime
roots
integers
function
+
–
320
views
1
answers
How would you solve the equation \(\dfrac{(v+2)^{2}-6}{3}=1\) ?
How would you solve the equation \(\dfrac{(v+2)^{2}-6}{3}=1\) ?
MathsGee
Platinum
113k
points
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asked
Sep 10, 2021
Mathematics
equation
calculate
real
calculus
solve
roots
quadratic
+
–
499
views
1
answers
How do you multiply two matrices?
How do you multiply two matrices?
Siyavula
Wooden Status
4.3k
points
Siyavula
asked
Sep 6, 2021
Mathematics
multiply
matrices
binomial
monomial
form
roots
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