If x²+px+q=0 and x²+qx+p=0,(p not =to q) have a common root. Show that 1+p+q=0; show that their other roots are the roots of the eqn x²+x+pq=0.

Question

If x²+px+q=0 and x²+qx+p=0,(p not =to q) have a common root. Show that 1+p+q=0; show that their other roots are the roots of the eqn x²+x+pq=0.

Answer 1

if

the roots of x²+px+q=0 are a and b, and
x²+qx+p=0 are a and c, then

ab = q
ac = p
a+b = -p
a+c = -q

b+p = c+q
q/a + p = p/a + q
(q-p)/a = q-p
a = 1

b=q
1+q = -p
1+p+q = 0

Take a crack at part 2.