Let and be the roots of

MATHEMATICS · Single correct · AoPS · Mathematics · Quadratic Equations - Part 1 · Quadratic Equations - Part 1

Problem

Let α\alpha and β\beta be the roots of 5x2−6x+1=05x^{2}-6x+1=0. The value of (α+β)2+αβ(\alpha+\beta)^{2}+\alpha\beta is (a) 4625\dfrac{46}{25} (b) 4125\dfrac{41}{25} (c) 3125\dfrac{31}{25} (d) 6125\dfrac{61}{25}

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