Answer
$||p||=\sqrt{20}$
$||q||=\sqrt{59}$
Work Step by Step
For distinct real numbers $t_0$ to $t_n$ and polynomial functions p and q in $P_n$, $\langle p,q\rangle=p(t_0)q(t_0)+...+p(t_n)q(t_n)$.
Therefore, for this problem, $||p||=\sqrt{\langle p,p\rangle}=\sqrt{p(-1)p(-1)+p(0)p(0)+p(1)p(1)}=\sqrt{16+0+4}=\sqrt{20}$
$||q||=\sqrt{\langle q,q\rangle}=\sqrt{q(-1)q(-1)+q(0)q(0)+q(1)q(1)}=\sqrt{25+9+25}=\sqrt{59}$
