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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.

Q2  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.

Answers (1)

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Let the roots of the polynomial be \alpha ,\beta \ and\ \gamma

\\\alpha +\beta +\gamma =2\\ \alpha \beta +\beta \gamma +\gamma \alpha =-7\\ \alpha \beta \gamma =-14

\\x^{3}-(\alpha +\beta +\gamma )x^{2}+(\alpha \beta +\beta \gamma +\gamma \alpha)x-\alpha \beta \gamma =0\\ x^{3}-2x^{2}-7x+14=0

Hence the required cubic polynomial is x3 - 2x2 - 7x + 14 = 0

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