Question:
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 are 5, −2 and −24 respectively.
Solution:
We know the sum, sum of the product of the zeroes taken two at a time and the product of the zeroes of a cubic polynomial then the cubic polynomial can be found as
x3 −(Sum of the zeroes)x2 + (sum of the product of the zeroes taking two at a time)x − Product of zeroes
Therefore, the required polynomial is
$x^{3}-5 x^{2}-2 x+24$
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