NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

The number of real roots of the equation 4 x x 2 + x + 3 + 5 x x 2 - 5 x + 3 = - 3 2 is equal to

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Correct answer

C. 2

Step-by-step solution

x = 0 is not a root. Dividing both the numerators and denominators by x and putting y = x + 3 x , we get, 4 y + 1 + 5 y - 5 = - 3 2 ⇒ y = - 5 , 3 x + 3 x = - 5 ⇒ x 2 + 5 x + 3 = 0 → two real roots x + 3 x = 3 ⇒ x 2 - 3 x + 3 = 0 → two imaginary roots ⇒ Total two real roots

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