JEE Main20198 Apr 2019Evening ShiftMathematicsQuadratic EquationActual

The number of integral values of m for which the equation, 1 + m 2 x 2 - 2 1 + 3 m x + 1 + 8 m = 0 has no real root, is

Options

A2
B3
CInfinitely many
D1

Correct answer

C. Infinitely many

Step-by-step solution

Since the given equation has no real solution. ⇒ D < 0 ⇒ 4 1 + 3 m 2 - 4 × 1 + m 2 1 + 8 m < 0 ⇒ 1 + 9 m 2 + 6 m - 1 + 8 m + m 2 + 8 m 3 < 0 ⇒ - 2 m 2 m - 1 2 < 0 Clearly, for infinite values of m given condition is true.

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