Question

Let $f\left(x\right)$ be a quadratic function given by the equation$f\left(x\right)=a{x}^2+bx+c$. The value of the function at point $x=-\frac{b}{2a}$ is less than zero.

If $a>0$, the nature of roots of the given equation are:

• A. Real and Equal
• B. Imaginary
• C. Real and Distinct
• D. Cannot be determined

Answer 1

The correct option is C Real and Distinct

The expression $b^2-4ac$ represent the discrimination of a quadrant function.If $a>0$ then graph will be on upward parabola and it will cut the $x-$axis a two distinct point indicating real and distinct roots. For real and distinct roots, the value of the discrimination is greater than zero.