Question

If alpha and beta are the zeroes of the quadratic polynomial f(x) = x2 - px + q, prove that alpha2/beta2 + beta2/alpha2= p4/q2 - 4p2/q + 2?

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quick answers and well explained steps ​

Answer 1

given,

         

alpha and beta are the zeroes of the quadratic polynomial f(x) = x² - px +q

then,

          α + β = -b/a

                   = p/1  = p

             

           αβ = c/a

                = q/1 = q

GIVEN,

              α²/β² + β²/α² = [ (α²)² + (β²)² ]/α²β²

           = [(α² + β²)² - 2α²β²]/α²β²

           = [(α + β)² - 2αβ - 2α²β²]/α²β²

           = [ p² - 2q - 2q² ]/q²

           =  p² - 2q² - 2q/q²

Answer 2

Answer:

done it's simple check the attached file