Answer
Zeros, each multiplicity 1:
$4+i,\quad 4-i$
Factorization:
$P(x)=(x-4-i)(x-4+i)$
Work Step by Step
$x^{2}-8x+17=0$
Quadratic formula:
$x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a},\quad a=1, b=-8, c=17$
$x=\displaystyle \frac{8\pm\sqrt{64-4(1)(17)}}{2(1)}=\frac{8\pm\sqrt{-4}}{2}$
$=\displaystyle \frac{8\pm 2i}{2}=\frac{2(4\pm i)}{2}=4\pm i$
Zeros, each multiplicity 1:
$4+i,\quad 4-i$
Factorization:
$1[x-(4+i)][x-(4-i)]=$
$P(x)=(x-4-i)(x-4+i)$
