Question : The value of $\lambda$ for which the expression $x^3 + x^2 - 5x + \lambda$ will be divisible by $(x-2)$ is:
Option 1: 2
Option 2: – 2
Option 3: – 3
Option 4: 4
Answer (1)
24th Jan, 2024
Correct Answer: – 2
Solution :
Given: $(x - 2)$ is a factor of the polynomial $P(x)= x^3 + x^2 - 5x + \lambda$
So, $P(2)=0$
⇒ $8 + 4 - 10 + λ = 0$
⇒ $λ + 2 = 0$
⇒ $λ= -2$
Hence, the correct answer is – 2.
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