Question

Find a cubic polynomial with the sum of its
zeroes, sum of the products of its zeroes taken
two at a time and the product of its zeroes as
2. -7 and -14 respectively.​

Answer 1

Answer:

the solution is in the attachment.

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Answer 2

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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