Q3 of 83 Page 76

If x = —1 is a root of x2 — px + q = 0, p, q ∈ R, prove that p + q + 1 = O.

As x = – 1 is a root of x2 — px + q = 0 hence x = – 1 will satisfy the equation x2 — px + q = 0


Put x = – 1 in x2 — px + q = 0


⇒ (– 1)2 – p × (– 1) + q = 0


⇒ 1 + p + q = 0


⇒ p + q + 1 = 0


Hence proved


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