Question

Which of the following is the set of roots of the quadratic equation $2x^2+5x-12=0?$

• A. $\{\frac{2}{3},-\frac{2}{3}\}$
• B. $\{\frac{3}{2},4\}$
• C. $\{\frac{3}{2},\frac{2}{3}\}$
• D. $\{\frac{3}{2},-4\}$

Answer 1

The correct option is D $\{\frac{3}{2},-4\}$

Given: $2x^2+5x-12=0$
Let $\alpha ,\beta$ be the roots of the equation $a{x}^2+bx+c=0$
$\Rightarrow \alpha =\frac{-b+\sqrt{D}}{2a}$

$\&\beta =\frac{-b-\sqrt{D}}{2a}$
$D=b^2-4ac$ is the discriminant of the equation.
$\Rightarrow D=5^2-4\left(2\right)(-12)=121$
$\Rightarrow \sqrt{D}=11$
$\therefore \alpha =\frac{-5+11}{2\times 2}=\frac{3}{2}\&\beta =\frac{-5-11}{2\times 2}=-4$