Question

Find the value of k if the quadratic equation $x^2+4x-k=0$ has real and distinct roots.

• A. $k<-4$
• B. $k>-4$
• C. $k\le -4$
• D. $k\ge -4$

Answer 1

The correct option is B

$k>-4$

We know that a quadratic equation has real and distinct roots if $D>0$
$\therefore b^2-4ac>0$

Comparing the given equation with the standard form of a quadratic equation, we have a = 1, b = 4 and c = -k

$\Rightarrow (4{)}^2-4(1\left)\right(-k)>0$
$\Rightarrow 16+4k>0$
$\Rightarrow 4k>-16$
$\Rightarrow k>-4$