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. 

Answer 1

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 x³ – 5x² – 2x + 24.