X^2+PX+1 is a factor of aX^3+bX+c

aX^3+bX+c has three roots.

Sum of roots = p+q+r(say) = 0
Product of roots = pqr = -c/a

Now X^2+PX+1 is its factor.

Sum of roots = p+q(say) = -P
Product of roots = pq = 1

Using these four results we can say that the third root is P which is further equal to -c/a

Putting this in aX^3+bX+c we get a^2 - c^2 = ab

Is this right?