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.
For a cubic polynomial equation, ax3 + bx2 + cx + d, and zeroes α, β and γ
we know that
Let the polynomial be ax3 + bx2 + cx + d, and zeroes α, β and γ.
A cubic polynomial with respect to its zeroes is given by,
x3 - (sum of zeroes) x2 + (Sum of the product of roots taken two at a time) x - Product of Roots = 0
x3 - (2) x2 + (- 7) x - (- 14) = 0
x3 - (2) x2 + (- 7) x + 14 = 0
Hence, the polynomial is x3 - 2x2 - 7x + 14.
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