Question

The equation (m being real), $m{x}^2+2x+m=0$ has two distinct roots if ______.

• A. m0
• B. m 0, 1
• C. m 1, – 1
• D. m 0, 1, –1

Answer 1

The correct option is B

m 0, 1

Step 1:- For, $m{x}^2+2x+m=0$, value of discriminant:
$D=(2{)}^2–4m^2=4-4m^2$

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

Step 3:- $4(1-m^2)>0$
$(1-m^2)>0$
$m^2<1$

$\Rightarrow -1<m<1$