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Maths Fundamental of Mathematics Graphs of Polynomial Subjective Type

Published on: August 13, 2026

Find the range of ' λ ' for which equation x 3 + x 2 – x – 1 – λ = 0 has 3 real solution.

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Sol. Let f(x) = x 3 + x 2 – x – 1 – λ

f'(x) = 3x 2 + 2x – 1 = 0 ⇒ x = – 1,

f(–1) = – λ , f(1/3) = – λ ⇒ (– λ ) < 0

⇒ λ ∈

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