Question

$a{x}^2+bx+c=0$, where a, b, c are real, has real roots if.

• A. a, b, c are integers
• B. $b^2>4ac$
• C. $ac<0$ and b is zero
• D. $c=0$

Answer 1

The correct option is B $b^2>4ac$

Given equation is $a{x}^2+bx+c=0$ where $a.b.c$ are real

Roots of this equation is given by $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x$ is real, if $\sqrt{b^2-4ac}$ is real.

if $b^2-4ac>0$

if $b^2>4ac$

Thus, $x$ is real iff $b^2>4ac$.

Hence, option B is correct.