NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

If x is rational and 4 x 2 + 1 x 2 + 1 6 x + 1 x - 5 7 = 0 , ⁡ then the product of all possible values of x is

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Correct answer

A. 4

Step-by-step solution

Given equation, 4 x 2 + 1 x 2 + 1 6 x + 1 x - 5 7 = 0 Let, x + 1 x = y ; x 2 + 1 x 2 = y 2 - 2 ⇒ 4 y 2 + 1 6 y - 6 5 = 0 ⇒ y = - 1 3 2 or ⁡ 5 2 When, y = 5 2 x + 1 x = 5 2 ⇒ x = 2 or 1 2 When, y = - 13 2 ⇒ x + 1 x = - 1 3 / 2 ⇒ 2 x 2 + 1 3 x + 2 = 0 ⇒ x = - 1 3 ± 1 5 3 4 Since x is rational, x = 2 or 1 2

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