The equation (m being real), mx2+2x+m=0 has two distinct roots if ___.
m ≠ 1, – 1
On comparing mx2+2x+m=0 with standard form ax2+bx+c=0, we get
a = m, b = 2 and c = m
Discriminant, D = b2−4ac
⇒D=(2)2–4m2=4−4m2
The roots of quadratic equation are distinct only when D≠0.
⇒4−4m2≠0
⇒m2≠1
⇒m≠±1
Therefore, the quadratic equation mx2+2x+m=0 has two distinct roots if m≠±1.