If the equation has exactly two solutions then a can not h…

Maths Inverse Trigonometric Functions Mix Single Correct MCQ

Published on: August 12, 2026

If the equation has exactly two solutions then a can not have the integral value -

-1

Text Solution

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The correct answer is:

CHECK THE SOLUTION.

(a, c, d)

The given equation holds if x 2 + x + 1 = ax + 1 and

– 1 ≤ x 2 +x + 1 ≤ 1

⇒ x (x + 1 + a) = 0 and – 1 ≤ x ≤ 0

⇒ x = 0 or a – 1 and – 1 ≤ x ≤ 0

∴ x = 0 is one solution and for another different solution

– 1 ≤ a –1 < 0

⇒ 0 ≤ a < 1 . So only integral value a can have is 0.

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