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Question
Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively
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Solution
Let the polynomial be ax3 + bx2 + cx + d and the zeroes be α, β and γ
Then, α + β + γ = `(2)/1 = (-b)/a`
αβ + βγ + γα = `(-7)/1 = c/a`
αβγ = `(-14)/1 = (-d)/a`
∴ a = 1, b = -2, c = -7 and d = 14
Hence, the polynomial is x3 - 2x2 - 7x + 14
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