Question

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

• A. m = 1
• B. m < 1
• C. m > 1
• D. m = 2

Answer 1

The correct option is B m < 1

Step 1 : For, $x^2+2x+m=0$,
$\Rightarrow a=1,b=2,c=m$

We know that

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

Step 2 : The roots of a quadratic equation are real and distinct only when $D>0$

Step 3 : $4-4m>0$

$4>4m$

$m<1$