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Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Let (log 2 x) 2 – 4log 2 x – m 2 – 2m–13 = 0 is an equation in x & m ∈ R, then which of the following is true

For any m ∈ R the equation has two distinct solutions

The product of solution of equation does not depend on m

One of the solutions of equation is less than 1 & other is greater than 1 for ∀ m ∈ R

The minimum value of the larger solution is 2 6 & maximum value of smaller solution is 2 –2

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(a, b, c, d)

Let log 2 x = t

⇒ t 2 – 4t – (12 + (m + 1) 2 ) = 0

t = 4 ± ±

D > 0 so there will be two distinct solution

Now sum of roots

t 1 + t 2 = 4

1og 2 x 1 x 2 = 4

⇒ x 1 x 2 = 16

Now D min. occurs when m = – 1

log 2 x = = 6, – 2

x = 2 6 , 2 –2 (c & d)

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