Question

Given that alpha and bitter are the roots of 2xsquare subtract 6x subtract 1 equal to 0.find the value of 2alpha bitter square plus 2 alpha square bitter plus 2 alpha bitter

Answer 1

alpha and beta are α,β

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2x^2 - 6x - 1 = 0
2αβ^2 + 2α^2β + 2αβ = 2αβ(α+β+1)

The roots are 3±√11
αβ = (3+√11)(3-√11) = 9-11 = -2
α+β = 3+√11 + 3-√11 = 6

Now finish it off