The sum of roots of equation x^2+px+q=0 is equal to sum of their squares, then prove that: p(p+1)=2q

Let a and b be
the roots of the equation. Hence, 

`a^2 + ap + q = 0` and

`b^2 +pb + q = 0`

We know that `a + b = a^2 + b^2` . Adding the two
equations yield:``

`a^2 + ap + q + b^2 + pb + q = 0`

Hence,

`a^2 + b^2 + (a + b)p + 2q = 0`

But `a +
b = a^2 + b^2` and...