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Question
If α, β and γ are the roots of the cubic equation x3 + 2x2 + 3x + 4 = 0, form a cubic equation whose roots are `- alpha, -beta, -γ`
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Solution
The given roots are – α, – β, – γ
The cubic equation is
x3 – x2 (– α – β – γ) + x(αβ + βγ + γα) + (αβγ) = 0
⇒ x3 + x2 (α + β + γ) + x(αβ + βγ + γα) + (αβγ) = 0
⇒ x3 + x2 (– 2) + x(3) – 4 = 0
⇒ x3 – 2x2 + 3x – 4 = 0
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