CAT 2019 Slot 1 — QA Question 15

Since we have |x|, we will have to consider cases where, x < 0 or x = 0 or x > 0.

For x > 0: 6$x^2$ + 1 = 5x ⇒  6$x^2$ − 5x + 1 = 0. The two roots of this equation are 1/2 and 1/3.

For x = 0, LHS = RHS, ∴ x = 0 is a root of the equation.

For x < 0: 6$x^2$ + 1 = −5x ⇒  6$x^2$ + 5x + 1 = 0. The two roots of this equation are −1/2 and −1/3.

∴ Number of roots = 2 + 1 + 2 = 5.

Answer: 5.