Question

If ............, then the quadratic equation does not have real solution.

• A. $D=0$
• B. $D>0$
• C. $D<0$
• D. $D\ge 0$

Answer 1

Answer: (C)

$D<0$

The general form of quadratic equation is given by $a{x}^2+bx+c=0$ ... $\left(i\right)$

Let $\alpha ,\beta$ be roots of quadratic equation $\left(i\right)$

$\alpha =\frac{-b-\sqrt{b^2-4ac}}{2a}$ and $\beta =\frac{-b+\sqrt{b^2-4ac}}{2a}$

The expression $D=b^2-4ac$ is the discriminant

If $D>0$, then $\alpha$ and $\beta$ are real.

If $D=0$, then $\alpha =\beta$

If $D<0$, then $\alpha$ and $\beta$ are not real.

So, when $D<0$, the quadratic equation does not have any real roots.

Hence, option C is correct.