Given a matrix P such that 
\begin{bmatrix} 1 & 1 & 1 \\ 0 & a & b \\a & 0 &b \end{bmatrix}

If P has eigen values 0 and 3 , then to determine value of a and b ? 

I have taken c as my third eigen value and formed two ewuations as

$a + b +1 = b +c $ using trace =sum of eigen values 

And $2ab - a^{2} =0$

How do i proceed from here .Thanks