Correct Answer - Option 2 : 7
Given:
x + 5 is a factor of the polynomial x3 + ax2 + ax - 15
Concept:
If x + α is a factor of polynomial P(x), where
P(x) = a1xn + a2xn - 1 + .......an - 1 + an
Then
P(α) = 0
Calculation:
Let
P(x) = x3 + ax2 + ax - 15
According to the question, x + 5 is a factor of a polynomial, hence
P(-5) = 0
⇒ (-5)3 + a(-5)2 + a(-5) - 15 = 0
⇒ - 125 + 25a - 5a - 15 = 0
⇒ 20a = 140
⇒ a = 7