Question

Find the roots of the following quadratic equation by factorisation method.

$9x^2-10x-8=0$

• A. The roots are $\frac{-8}{3}and4$.
• B. The roots are $\frac{-2}{3}and2$.
• C. The roots are $\frac{-5}{3}and4$.
• D. The roots are $\frac{-2}{3}and4$.

Answer 1

The correct option is D

The roots are $\frac{-2}{3}and4$.

$9x^2-10x-8=0$
$\Rightarrow 9x^2-12x+2x-8=0$ [by splitting the middle term]

$\Rightarrow 3x(x-4)+2(x-4)=0$
$\Rightarrow (3x+2)(x-4)=0$
$Now,3x+2=0$
$\Rightarrow x=-\frac{2}{3}$
$andx-4=0$
$\Rightarrow x=4$
Hence, the roots of the equation $(x-4)(x+\frac{2}{3})=0$ are $\frac{-2}{3}and4$.