Question

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

• A. m$\ne$0
• B. m $\ne$ 0, 1
• C. m $\ne$ 1, – 1
• D. m $\ne$ 0, 1, –1

Answer 1

The correct option is C

m $\ne$ 1, – 1

On comparing $m{x}^2+2x+m=0$ with standard form $a{x}^2+bx+c=0$, we get

a = m, b = 2 and c = m

Discriminant, D = $b^2-4ac$

$\Rightarrow D=(2{)}^2–4m^2=4-4m^2$

The roots of quadratic equation are distinct only when $D\ne 0$.

$\Rightarrow 4-4m^2\ne 0$

$\Rightarrow m^2\ne 1$

$\Rightarrow m\ne \pm 1$

Therefore, the quadratic equation $m{x}^2+2x+m=0$ has two distinct roots if $m\ne \pm 1$.