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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.
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25/05/2021 1:14 pm
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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.
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25/05/2021 1:15 pm
Let us consider the cubic polynomial is ax^{3 }+ bx^{2 }+ cx + d and the values of the zeroes of the polynomials be α, β, γ.
As per the given question,
α+β+γ = b/a = 2/1
αβ +βγ+γα = c/a = 7/1
α βγ = d/a = 14/1
Thus, from above three expressions we get the values of coefficient of polynomial.
a = 1, b = 2, c = 7, d = 14
Hence, the cubic polynomial is x^{3}2x^{2}7x+14
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