2006
Problem - 3609
Let $r_1, \cdots, r_5$ be the roots of the polynomial $x^5 + 5x^4 - 79x^3 +64x^2 + 60x+144$. What is $r_1^2 +\cdots + r_5^2$?
By the Vieta's theorem, we have
$$r_1^2+\cdots+r_5^2=(r_1+\cdots+r_5)^2-2(r_1r_2+\cdots+r_4r_5)=(-5)^2-2\times(-79)=\boxed{183}$$