Question

If alpha and beta are the zeros of quadratic polynomial 4x2-5x-1 find the value of alpha/beta+beta/alpha

Answer 1

4x^2 - 5x - 1

a = 4

b = -5

c = -1

α + β = -b / a = 5 / 4

α * β = -1 / 4

α / β + β / α = (α^2 + β^2)/αβ

= ( α + β)^2 - 2αβ

= (5/4)^ 2 - 2*(-1/4)

= 25/16 + 1/2

= 66 / 32

= 33 / 16

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