Question

The sum of all the real values of x satisfying the equation  2^{(x - 1)(x2 + 5x - 50)} = 1  is

(A)  -5

(B)  14

(C)  -4

(D)  16

Answer 1

Correct option  (C)  -4

The sum of all the real values of x satisfying the equation 2^{(x - 1)(x2 + 5x - 50)} = (1)⁰, we have

(x - 1)(x² + 5x - 50) = 0

Therefore,

x - 1 = 0, x² + 5x - 50 = 0

⇒ x = 1, x² + 10x - 5x - 50 = 0

⇒ x(x + 10) - 5(x + 10) = 0

⇒ (x + 10) (x - 5) = 0

⇒ x = -10, 5

Therefore, the sum of all the real values of x, we get -10 + 5 + 1 = -4