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Find a cubic polynomial with the sum, sum of the product of it

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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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.

10 mins ago

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Text solutionVerified

Let the polynomial be

a x^{3} + b x^{2} + c x + d

and the zeroes be

α, β, γ

.
Sum of the polynomial =

α + β + γ = \frac{2}{1} = \frac{- b}{a}

Sum of the product of its zeroes taken two at a time =

α β + β γ + α γ = \frac{- 7}{1} = \frac{c}{a}

Product of the root =

α β γ = \frac{- 14}{1} = \frac{- d}{a}

a = 1, b = - 2, c = - 7, d = 14.

Hence the polynomial is

x^{3} - 2 x^{2} - 7 x + 14

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Question Text	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.
Answer Type	Text solution:1
Upvotes	151