Find a cubic polynomial with the sum of its zeroes, sum of the product

1.	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» As we know, General form of a cubic polynomial whose zeroes are a, b and c is: x³ – (a + b + c) x² + (ab + bc + ca)x – abc Also written as : x³ – (Sum of the zeros) x² + (Sum of the product of the zeros taking two at a time) x – (Product of Zeros) …(1) Given: Sum of the zeros = 5 Sum of the product of its zeros taken two at a time -2 Product of its zeros = –24 Putting these values in the equation (1), we get: x³ – 5x² – 2x + 24 Which is required polynomial.

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»

As we know, General form of a cubic polynomial whose zeroes are a, b and c is:

x³ – (a + b + c) x² + (ab + bc + ca)x – abc

Also written as :

x³ – (Sum of the zeros) x² + (Sum of the product of the zeros taking two at a time) x – (Product of Zeros) …(1)

Given:

Sum of the zeros = 5

Sum of the product of its zeros taken two at a time -2

Product of its zeros = –24

Putting these values in the equation (1), we get:

x³ – 5x² – 2x + 24

Which is required polynomial.