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JEE Main20236 Apr 2023Morning ShiftMathematicsQuadratic EquationActual

The sum of all the roots of the equation x 2 - 8 x + 15 - 2 x + 7 = 0 is

Options

  1. A9 - 3
  2. B9 + 3
  3. C11 - 3
  4. D11 + 3

Correct answer

B. 9 + 3

Step-by-step solution

Given, x 2 - 8 x + 15 - 2 x + 7 = 0 Now taking Case: I when, x 2 - 8 x + 15 ≥ 0 ⇒ ( x - 3 ) ( x - 5 ) ≥ 0 ⇒ x ≤ 3 OR x ≥ 5 x 2 - 8 x + 15 - 2 x + 7 = 0 ⇒ x 2 - 8 x + 15 - 2 x + 7 = 0 ⇒ x 2 - 10 x + 22 = 0 ⇒ x = 5 + 3 ,   5 - 3   rejected So, α = 5 + 3 Now taking Case: II when, x 2 - 8 x + 15 - 2 x + 7 = 0 ⇒ x 2 - 8 x + 15 < 0 ⇒ 3 < x < 5 ⇒ x 2 - 8 x + 15 + 2 x - 7 = 0 ⇒ x 2 - 6 x + 8 = 0 ⇒ x = 4 ,   2

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