# arrow_back Prove that, for all values of $x$, $x^{2}+4 x+12>x+3$

29 views
Prove that, for all values of $x$,
$x^{2}+4 x+12>x+3$

\begin{aligned} &x^{2}+4 x+12>x+3 \\ &x^{2}+3 x+9>0 \\ &\left(x+\frac{3}{2}\right)^{2}-\frac{9}{4}+9>0 \\ &\left(x+\frac{3}{2}\right)^{2}+\frac{27}{4}>0 \end{aligned}
Min point at $\left(-\frac{3}{2}, \frac{27}{4}\right)$
$\therefore x^{2}+4 x+12>x+3$ for all values of $x$
by Platinum
(106,844 points)

## Related questions

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
How will I prove that the roots of $m(x^2-1)=5x$ are real for all real values of $m, (m\neq0)$?
How will I prove that the roots of $m(x^2-1)=5x$ are real for all real values of $m, (m\neq0)$?This question is from the gr.11 CAPS syllabus under the section Nature of the Roots. The question in Latex (using the provided tools): How will I pr ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Having x^2 +bx + k(x^2 + 3x + 2) = 0, Show that the discriminant is given by: k2 + 6bk + b^2 + 8
Having x^2 +bx + k(x^2 + 3x + 2) = 0, Show that the discriminant is given by: k2 + 6bk + b^2 + 8Having x^2 +bx + k(x^2 + 3x + 2) = 0, Show that the discriminant is given by: &nbsp;k2 + 6bk + b^2 + 8 ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Grade 12 Paper 1 - Prove that $\sum_{k=1}^{\infty} 4.3^{2-k}$ is a convergent geometric series. Show ALL your calculations.
Grade 12 Paper 1 - Prove that $\sum_{k=1}^{\infty} 4.3^{2-k}$ is a convergent geometric series. Show ALL your calculations.Prove that $\sum_{k=1}^{\infty} 4.3^{2-k}$ is a convergent geometric series. Show ALL your calculations. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that the roots of the equation x^2 - (a + b) x + ab - p^2 = 0 are real for all real values of a, b and p.
Prove that the roots of the equation x^2 - (a + b) x + ab - p^2 = 0 are real for all real values of a, b and p.Prove that the roots of the equation x^2 - (a + b) x + ab - p^2 = 0 are real for all real values of a, b and p. ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: $$2y = x^{2} + 1$$
$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: $$2y = x^{2} + 1$$$1 ; y ; b$ are the first 3 terms of an arithmetic sequence and $1; x ; b$ are the first 3 terms of a geometric sequence. Prove that: 2y = x^{2} + ...
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
For which values of $x$ will $\sum_{k=1}^{\infty}(4 x-1)^{k}$ exist.
For which values of $x$ will $\sum_{k=1}^{\infty}(4 x-1)^{k}$ exist.For which values of $x$ will \ \sum_{k=1}^{\infty}(4 x-1)^{k} \ exist. ...
Grade 12 - Paper 1 - If $\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of $p$.
Grade 12 - Paper 1 - If $\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of $p$.If $\sum_{k=p}^{\infty} 4.3^{2-k}=\frac{2}{9}$, determine the value of $p$. ...