Question

Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and product of its zeroes as the numbers given below:

2, – 7, – 14

Answer 1

Let the zeroes be α, β and γ.

Then, we have

α + β + γ = 2

αβ + βγ + γα = – 7

and αβγ = – 14

Now, required cubic polynomial

Sox³ – 2x² – 7x + 14 is the required cubic polynomial.