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Question

The equation (m being real), mx2+2x+m=0 has two distinct roots if ___.


A

m0

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B

m 0, 1

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C

m 1, – 1

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D

m 0, 1, –1

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Solution

The correct option is C

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 = b24ac

D=(2)24m2=44m2

The roots of quadratic equation are distinct only when D0.

44m20

m21

m±1

Therefore, the quadratic equation mx2+2x+m=0 has two distinct roots if m±1.


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