Question

if alpha and beta are the zeros of the quadratic polynomial X square + 2 X + 1 then find the quadratic polynomial whose zeros are Alpha square beta and alpha beta square

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.

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