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Maths Quadratic Equations Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 11, 2026

= has -

Exactly two real roots

No real root

One irrational root

None of these

Text Solution

Verified by Experts

The correct answer is:

Taking log of the sides in (1), we get

⇒ log 2 x = log 2 ( )

⇒ y = log 2 2 where y = log 2 x

⇒ 3y 3 + 4y 2 – 5y – 2 = 0

⇒ 3y 3 – 3y 2 + 7y 2 – 7y + 2y – 2 = 0

⇒ ( y – 1) (3y 2 + 7y + 2) = 0

⇒ ( y – 1) [3y 2 + 6y + y + 2] = 0

(y – 1) (y + 2) (3y + 1) = 0

⇒ y = 1, – 2, – 1/3

⇒ log 2 x = 1, – 2, – 1/3 ⇒ x = 2, , 2 –1/3

Thus, (1) has one irrational root viz. 2 –1/3 .

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