The number of real roots of the equation x x - 5 x + 2 + 6 = 0 , is

Step-by-step solution

Given, x x - 5 x + 2 + 6 = 0 Now taking case 1 when x < - 2 we get, - x 2 + 5 x + 10 + 6 = 0 ⇒ x 2 - 5 x - 16 = 0 ⇒ x = 5 - 89 2 , ignoring x = 5 + 89 2 as x < - 2 , so one solution is possible here, Now taking case 2 when - 2 ≤ x < 0 we get, - x 2 - 5 x - 10 + 6 = 0 ⇒ x 2 + 5 x + 4 = 0 ⇒ x = - 1 , ignoring x = - 4 as - 2 ≤ x < 0 Now taking case 3 , when x ≥ 0 we get, x 2 - 5 x - 10 + 6 = 0 ⇒ x 2 - 5 x - 4 = 0 ⇒ x = 5 + 41 2 , ignoring x = 5 - 41