Question

The sum of all real values of x satisfying the equation (x2 - 5x + 5)x2 + 4x - 60 = 1

A) 5

(B) 3

(C) −4

(D) 6

Answer 1

Correct option**(B) 3**

We have

(x2 - 5x + 5)x2 + 4x - 60 = 1

Case 1: x2 + 4x − 60 = 0

(x + 10) (x − 6) = 0 ⇒ x = −10, 6

Case 2:x2 − 5x + 5 = 1

or x2 − 5x + 5 = −1

⇒ x2 − 5x + 4 = 0

⇒ x2 − 5x + 6 = 0

⇒ x = 1, 4

⇒ x = 2 and 3 x2 + 4x − 60 must be even number for x = 2 and 3. Substituting the two values in x2 + 4x − 60, we get

4 + 8 − 60 = −48

9 + 12 − 60 = −39

Value of x can not be 3 because x2 + 4x − 60, is negative at x = 3. Thus, the sum of all value of x

= −10 + 6 + 1 + 4 + 2 = 3