Let be real roots of the quadratic equation

MATHEMATICS · Single correct · AoPS · Mathematics · More Inequalities · More Inequalities

Problem

Let

\alpha, \beta

be real roots of the quadratic equation

x^2 + kx + (k^2 + 2k - 4) = 0

, then the minimum value of

\alpha^2 + \beta^2

is equal to: (a) 12 (b)

\frac{4}{9}

(c)

\frac{16}{9}

(d)

\frac{8}{9}