Prove That If the equation x^2+ax+b=0 and cx^2+2ax-3b=0 have a common root then b=5a^2(c-2)/(c+3)^2

Answer 1

do a synthetic division on each polynomial using x-p.
If p is a common root, then both remainders will be zero.

Eliminate p and you will wind up with a polynomial in a,b,c.

Solve for b.