NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

If both the roots of the equation 4 x 2 - 2 x + m = 0 lie in the interval - 1,1 , then

Options

A- 3 < m < - 2
B0 < m < 2
C2 < m < 5 2
D- 2 < m ≤ 1 4

Correct answer

D. - 2 < m ≤ 1 4

Step-by-step solution

Coefficient of x 2 is positive So, D ≥ 0 , f 1 > 0 , f - 1 > 0 D ≥ 0 ⇒ 4 - 4 × 4 × m ≥ 0 ⇒ m ≤ 1 4 f - 1 > 0 ⇒ 4 + 2 + m > 0 ⇒ m > - 6 f 1 > 0 ⇒ 4 - 2 + m > 0 ⇒ m > - 2 Taking intersection we get m ∈ - 2 , 1 4

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