Problem: If rrr and sss are the roots of x2−px+q=0x^{2}-p x+q=0x2−px+q=0, then r2+s2r^{2}+s^{2}r2+s2 equals:
Answer Choices:
A. p2+2qp^{2}+2 qp2+2q
B. p2−2qp^{2}-2 qp2−2q
C. p2+q2p^{2}+q^{2}p2+q2
D. p2−q2p^{2}-q^{2}p2−q2
E. p2p^{2}p2 Solution:
r2+s2=(r+s)2−2rs=p2−2qr^{2}+s^{2}=(r+s)^{2}-2 r s=p^{2}-2 qr2+s2=(r+s)2−2rs=p2−2q.