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Question -

Find a cubic polynomial with the sum, sum ofthe product of its zeroes taken two at a time, and the product of its zeroes as2, –7, –14 respectively.



Answer -

Solution:

Let us consider the cubic polynomial is ax3+bx2+cx+dand 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 thevalues 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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