Question

If the roots of a quadratic equation are $-2,8$ then which of the following is true regarding the discriminant $\left(D\right)$ ?

• A. $D=0$
• B. $D<0$
• C. None of these
• D. $D>0$

Answer 1

The correct option is D $D>0$

For quadratic equation $a{x}^2+bx+c=0,a\ne 0$ Nature of roots is given by discriminant $D=b^2-4ac$ as $\left(i\right)D>0\Rightarrow \text{Real and distinct roots}\left(ii\right)D=0\Rightarrow \text{Real and equal roots}\left(iii\right)D<0\Rightarrow \text{Non real or imaginary roots}$

The given roots are $-2,8$
$\Rightarrow$ The roots are real and distinct
$\therefore$ Discriminant $D>0$