Question

If alpha and beta are the zeroes of the quadritic polynomial x2+ 2x+ 1,then find the quadritic polynomial whose zeroes alpha2beta and alphabeta2

Answer 1

Sol:
Given that α and β are the zeroes of the polynomial x2 - 2x - 15 then
α + β = 2 and αβ = -15

If 2α, 2β are zeros of the quadratic polynomial then the equation is
x2 - 2(α + β)x + 4αβ =0 then

Sum of roots = 2(α + β) = 4
Product of roots = 4αβ = -60
Now the polynomial equation is
x2 - 4x - 60 =0.