NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

The least integral value of a for which the graphs y = 2 a x + 1 and y = a - 6 x 2 - 2 do not intersect is

Options

A- 6
B- 5
C3
D2

Correct answer

B. - 5

Step-by-step solution

a - 6 x 2 - 2 = 2 a x + 1 a - 6 x 2 - 2 a x - 3 = 0 Since the graphs do not intersect, ∴ D < 0 ⇒ 4 a 2 + 4 × 3 a - 6 < 0 ⇒ a 2 + 3 a - 18 < 0 ⇒ a + 6 a - 3 < 0 ⇒ a ∈ - 6 , 3 Hence, the least integer value of a is - 5

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