Question

What is the condition for the quadratic equation $x^2+bx+c=0$ to have real roots?

• A. $b^2<-4c$
• B. $b^2>4c$
• C. $b^2\ge 4c$
• D. $b^2=4c$

Answer 1

The correct option is C $b^2\ge 4c$

The discriminant of the quadratic equation $a{x}^2+bx+c=0$, where a, b, c are real numbers is $D=b^2-4ac$.
Thus, the discriminant of the equation $x^2+bx+c=0is{b}^2-4\left(1\right)\left(c\right)=b^2-4c$.

For real roots, $D\ge 0$.
Hence, $b^2-4c\ge 0$.
$\Rightarrow b^2\ge 4c$