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Write the value of λ for which $x 2$ + 4x + λ, is a perfect square.

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answer is A.

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Detailed Solution

Given,

x 2

+ 4x + λ
Compare the equation

x 2 + 4 x + λ = 0 with a x 2 + b x + c = 0

a = 1 b = 4 c = λ

For the given equation to be perfect square, the roots should be equal.
Therefore, the discriminant is 0.

⇒ b 2 − 4 a c = 0 ⇒ 42 − 4 ⋅ 1 ⋅ λ = 0 ⇒ 16 − 4 λ = 0 ⇒ 4 λ = 16 ⇒ λ = 4

For

x 2 + 4 x + λ = 0

to be a perfect square, the value of

λ

must be 4.
Hence, the correct option is 1.

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