If α and β are the zeroes of a polynomial such that α + β = -6 and

1.	If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.
Answer» Given : α + β = -6 = sum of zeros and αβ = 5 = Product of zeroes We know that, if α and β are the zeros of the polynomial then the quadratic polynomial can be x² – (α + β) x + αβ Now substituting the values, we get x² – (-6)x + 5 = x² + 6x + 5, which is required polynomial.

If α and β are the zeroes of a polynomial such that α + β = -6 and αβ = 5, then find the polynomial.

Answer»

Given : α + β = -6 = sum of zeros and αβ = 5 = Product of zeroes

We know that, if α and β are the zeros of the polynomial then the quadratic polynomial can be x² – (α + β) x + αβ

Now substituting the values, we get

x² – (-6)x + 5

= x² + 6x + 5, which is required polynomial.