Question

If the value of '$b^2-4ac$'is equal to zero, the quadratic equation $a{x}^2+bx+c=0$ will have

• A. Two real roots which are equal
• B. Two Distinct Real Roots.
• C. No Real Roots.
• D. No Roots or Solutions.

Answer 1

The correct option is A Two real roots which are equal

$a{x}^2+bx+c=0$

For roots, $D\equiv b^2-4ac$

and given that $b^2-4ac=0$

$\Rightarrow D=0$

SO, equation will have only one root as,

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2\left(a\right)}$

$x=\frac{-b\pm 0}{2a}$

$x=\frac{-b}{2a}$ Only one real root.