#### Question

Write the value of λ for which x^{2} + 4x + λ is a perfect square.

#### Solution

The given quadric equation is x^{2} + 4x + λ = 0

Then find the value of *k.*

Here, a =1, b= 4 and, c = λ

As we know that D = b^{2} - 4ac

Putting the value of a =1, b = 4 and, c = λ

` = (4)^2 - 4 xx 1 xx λ`

= 16 -4λ

The given equation are perfect square, ifD = 0

14 - 4λ = 0

4λ = 16

`λ = 16/4`

= 4

Therefore, the value of **λ = 4.**

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#### APPEARS IN

Solution Write the Value of λ for Which X2 + 4x + λ is a Perfect Square. Concept: Solutions of Quadratic Equations by Completing the Square.