Question

If the equation $x^2+4x-k=0$ has real and distinct roots, then :

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

Answer 1

The correct option is B $k>-4$

Since the quadratic equation has real and distinct roots, then $D>0$
$\therefore b^2-4ac>0$
$\Rightarrow (4{)}^2-4(1\left)\right(-k)>0$
$\Rightarrow 16+4k>0$
$\Rightarrow 4k>-16$
$\Rightarrow k>-4$