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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 5, -2 and -24 respectively.
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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 `x^3` – (sum of the zeroes)`x^2` + (sum of the product of the zeroes taking two at a time)x – product of zeroes Therefore, the required polynomial is
`x^3 – 5x^2 – 2x + 24`
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