NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

The sum of the roots of the equation x 2 - x - 6 = x + 2 is

Options

A0
B- 2
C2
D4

Correct answer

D. 4

Step-by-step solution

x 2 - x - 6 = x + 2 x - 3 Case i x < - 2 or x ≥ 3 x 2 - x - 6 = x + 2 ⇒ x 2 - 2 x - 8 = 0 x - 4 x + 2 = 0 ⇒ x = - 2,4 ⇒ x = 4 in this case Case i i - 2 ≤ x < 3 - x 2 + x + 6 = x + 2 ⇒ x 2 = 4 ⇒ x = ± 2 ⇒ x = - 2,2 in this case ∴ The roots are - 2,2 , 4 ⇒ s u m of roots = 4

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