Use a purely imaginary root to factor and transform a quartic

The equation $z^4-4z^3+az^2-20z+25=0$, $a\in\mathbb R$, has a root $ki$ with $k\in\mathbb R$.

(i) Explain clearly why more than one value of $k$ is possible.1 mark

(ii) Find the possible exact values of $k$, show that $a=10$, and hence find the roots.7 marks

(iii) Deduce the roots in Cartesian form of (a) $w^4+4iw^3-10w^2-20iw+25=0$ and (b) $25v^4-20v^3+10v^2-4v+1=0$.4 marks