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99 Percentile Qs Bank for JEE MainMathematicsQuadratic Equation

The sum of all real values of x satisfying the equation x 2 - 5 x + 5 x 2 + 4 x - 60 = 1 is

Options

  1. A6
  2. B5
  3. C3
  4. D- 4

Correct answer

C. 3

Step-by-step solution

The given equation will be true in 3 cases. Case 1: when x 2 - 5 x + 5 = 1 ⇒ x 2 - 5 x + 4 = 0 ⇒ x = 1 , 4 Case 2: when x 2 + 4 x - 60 = 0 ⇒ x = 6 , - 10 Case 3: when x 2 - 5 x + 5 = - 1 and x 2 + 4 x - 60 ∈ even integers Now, x 2 - 5 x + 5 = - 1 ⇒ x = 2 , 3 Only x = 2 satisfies the given condition, Hence, sum of all real values of x is 1 + 4 + 6 - 10 + 2 = 3

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