Question

If the value of the discriminant of the quadratic equation $a{x}^2+bx+c=0$ is less than $0$, then the nature of the roots is ____

Answer 1

When $a,b$ and $c$ are real numbers , $a\ne 0$ and discriminant is negative $($ i.e. $b^2-4ac<0$ $)$, then the roots $\alpha$ and $\beta$ of the quadratic equation $a{x}^2+bx+c=0$ are unequal and imaginary. Here the roots $\alpha$ and $\beta$ are pair of the complex conjugates.