If the fraction reduces to a quotient of two linear functi…

Maths Quadratic Equations Solution of Quadratic Inequations and Miscellaneous Equations Numeric Response

Published by: CGP EDU Academic Team

Published on: August 13, 2026

If the fraction reduces to a quotient of two linear functions then a equals………

Text Solution

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The correct answer is:

(8)

Sol. Let N r = f(x) = x 3 + (a – 10)x 2 – x + a – 6 = 0 has roots α, β, γ

& D r = g(x) = x 3 + (a – 6)x 2 – x + a – 10 = 0 has roots α, β, ρ

∴ f(x) – g(x) = – 4x 2 + 4 = 0

⇒ x = ± 1

∴ α + β = 0, αβ = – 1

∴ α + β + γ = – (a – 10) = 10 – a

∴ ⇒ γ = 10 – a………..(i)

αβγ = 6 – a ⇒ γ = a – 6………..(ii)

from (i) & (ii)

10 – a = a – 6

a = 8

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