Question

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

• A. $b^2+4ac\ge 0$
• B. $b^2-4ac>0$
• C. $b^2\ge -4c$
• D. $b^2\ge 4c$

Answer 1

The correct option is C

$b^2\ge -4c$

For the equation $a{x}^2+bx+c=0$ to have real roots, the discriminant(D) must be greater than or equal to zero.
$D\ge 0$
$D=b^2-4ac$
$\Rightarrow b^2-4ac\ge 0$
For the given equation, $a=1,b=b$ and $c=-c$
$\Rightarrow b^2+4c\ge 0$
$\Rightarrow b^2\ge -4c$