10. $x^{2}+4 x+8=0$ has roots $a$ and $b$. Find a quadratic polynomial with integer coefficients whose roots are $\frac{1}{a}$ and $\frac{1}{b}$.
(ans. $8 x^{2}+4 x+1$.
$a b=8, a+b=-4 \Rightarrow \frac{1}{a} \frac{1}{b}=\frac{1}{8}, \frac{a+b}{a b}=\frac{1}{a}+\frac{1}{b}=-\frac{1}{2}$. This means that the reciprocals are roots of the polynomial $x^{2}+\frac{1}{2} x+\frac{1}{8}$ and hence of $8 x^{2}+4 x+1$.)