CGP Edu

Maths Quadratic Equations Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If 0 < a < b < c < d, then the quadratic equation ax 2 + {1 – a(b + c)} x + abc – d = 0 (1) has-

Real and distinct roots out of which one lines between c and d

Real and distinct roots out of which one lines between a and b

Real and distinct roots out of which one lines between b and c

Non-real roots

Text Solution

Verified by Experts

The correct answer is:

We can rewrite (1) as

ax 2 – a(b + c)x + abc + x – d = 0

or a(x – b) (x – c) + x – d = 0

Let ƒ(x) = a(x – b) (x – c) + x – d

As a > 0, y = ƒ(x) represents a parabola which open upwards. See Fig.

Also ƒ = b – d < 0

ƒ = c – d < 0, and ƒ = a(d – b) (d – c) > 0

Thus, ƒ(x) = 0 has root between – ∞ and b and between c and d.

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