Q. 24.3( 151 Votes )

# 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.

Answer :

For a cubic polynomial equation, ax^{3} + bx^{2} + cx + d, and zeroes α, β and γ

we know that

Let the polynomial be ax^{3} + bx^{2} + cx + d, and zeroes α, β and γ.

A cubic polynomial with respect to its zeroes is given by,

x^{3} - (sum of zeroes) x^{2} + (Sum of the product of roots taken two at a time) x - Product of Roots = 0

x^{3} - (2) x^{2} + (- 7) x - (- 14) = 0

x^{3} - (2) x^{2} + (- 7) x + 14 = 0

Hence, the polynomial is x^{3} - 2x^{2} - 7x + 14.

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