Question

For what value of $m$ does the equation, $x^2+2x+m=0$ have two distinct real roots?

• A. m < 1
• B. -1 < m < 1
• C. m = 1
• D. m >1

Answer 1

The correct option is A m < 1

For, $x^2+2x+m=0$,
$a=1,b=2,c=m$

We know, $D=b^2–4ac$
$\Rightarrow D=(2{)}^2–4m$
$=4-4m$

The roots of a quadratic equation are real and distinct only when $D>0$.

$\Rightarrow 4-4m>0$

$\Rightarrow 4>4m$

$\Rightarrow m<1$