Question

The zeroes of the polynomial $f\left(x\right)=6x^2-x-2$ is/are

• A. $\frac{2}{3}$
• B. $-\frac{2}{3}$
• C. $-\frac{1}{2}$
• D. $\frac{1}{2}$

Answer 1

Answer: (A), (C)

The correct options are
A $\frac{2}{3}$
C $-\frac{1}{2}$

Given,
$f\left(x\right)=6x^2-x-2$
$\Rightarrow f\left(x\right)=6x^2+3x-4x-2$
$\Rightarrow f\left(x\right)=3x(2x+1)-2(2x+1)$
$\Rightarrow f\left(x\right)=(3x-2)(2x+1)$

For zeroes of a polynomial,
$f\left(x\right)=0\Rightarrow (3x-2)(2x+1)=0\therefore x=-\frac{1}{2},\frac{2}{3}$