The cubic equation x 3 + 3x 2 - 1 = 0 has roots , , .
Question:
The cubic equation x3 + 3x2 - 1 = 0 has roots α, β, γ. Show that the cubic equation with roots α + 2/α, β + 2/β, γ + 2/γ is y3 – 3y2 – 9y + 3 = 0. Hence, determine the values of:
a. (α + 2)(β + 2)(γ + 2)/αβγ
b. α/α + 2 + β/β + 2 + γ/γ + 2
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Related Book For
Cambridge International AS & A Level Further Mathematics Coursebook
ISBN: 9781108403375
1st Edition
Authors: Lee Mckelvey, Martin Crozier
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