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Question

If one root of the equation x2λx+12=0 is even prime while x2+λx+μ=0 has equal roots, then μ is equal to

A
8
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B
16
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C
24
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D
32
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Solution

The correct option is C 16
We know that, the only even prime is 2.

2 is the root of x2λx+12=0

(2)2λ(2)+12=0

λ=8 ... (i)

and x2+λx+μ=0 has equal roots.

The roots are equal only when discriminant D=0 i.e. b24ac=0

λ24μ=0

or (8)24μ=0 ....... [from Eq. (i)]

μ=16

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