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2. 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.

2. 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.

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Solution: Let us consider the cubic polynomial is ax3+bx2+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 x3-2x2-7x+14

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