Question

Solve for \(x\) in \(12 x^{3}-4 x^{2}-5 x=0\)

Answer 1

\[12 x^{3}-4 x^{2}-5 x=0\]

start by factorizing with the common factor \(x\)

\[x\left(12 x^{2}-4 x-5\right)=0\]

Using the rule: If \(a\cdot b =0\) then \(a=0\) or \(b=0\) or both are equal to zero.

then,

 

\[\Rightarrow x=0\]

or

\[12 x^{2}-4 x-5=0\]

Using the quadratic formula:

\[x=\dfrac{\pm \sqrt{b^{2}-4 a c}}{2a}\]

\(a=12; b=-4; c=-5\)

\[x= \dfrac{-(-4) \pm \sqrt{(-4)^{2}-4(12)(-5)}}{2(12)}\]

\[= \dfrac{4 \pm \sqrt{256}}{24} \]

\[= \dfrac{4 \pm 16}{24}\]

\[= \dfrac{ 4 \pm 2}{3} \]

\(\therefore x=0 \quad \text{OR} \quad x=\dfrac{4+2}{3} \quad \text{OR} \quad x=\dfrac{4-2}{3}\)