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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 13, 2026

The equation x 4 – (m – 3)x 2 + m = 0 has

No real root if m ∈ (0, 1)

Four real and distinct roots if m > 9

No real root if m ∈ (0, 9)

Zero as its roots if m = 0

Text Solution

Verified by Experts

The correct answer is:

CHECK THE SOLUTION.

(b, c, d)

x 4 – (m – 3) x 2 + m = 0

if its all roots are real then roots of f(t) = t 2 – (m – 3) t + m = 0 must be non-negative.

i.e. D ≥ 0 ⇒ m ∈ (– ∞ , 1] ∪ [9, ∞ )

α + β > 0 ⇒ m – 3 > 0 ⇒ m > 3

αβ ≥ 0 ⇒ m ≥ 0

So, m ∈ [9, ∞ )

So, for four real and distinct roots m ∈ (9, ∞ ) as D = 0 at m = 9.

both roots of f(t) = 0 are negative for m ∈ (0, 3) & D < 0 for m ∈ (1, 9). Hence no root of given equation for m ∈ (0, 9)

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