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:

5/7, 1/7, 1/7

Answer 1

Let the zeroes be α, β and γ.

Then, we have

Now, required cubic polynomial

So, 7x³ – 5x² + x – 1 is the required cubic polynomial which satisfy the given conditions.