Question

If α and β are the roots of the polynomial f(x) = x² – 2x + 3, find the polynomial whose roots are α + 2, β + 2

Answer 1

α and β are the roots of the polynomial

x² – 2x + 3 = 0

α + β = 2; αβ = 3

Sum of the roots = α + 2 + β + 2

= α + β + 4

= 2 + 4

= 6

Product of the roots = (α + 2) (β + 2)

= αβ + 2α + 2β + 4

= αβ + 2(α + β) + 4

= 3 + 4 + 4

= 11

The quadratic polynomial

x² – (sum of the roots) x + product of the roots = 0

x² – (6)x + 11 = 0

x² – 6x + 11 = 0