Answer to Question #47937 in Algebra for doe

Question

factoring trinomials

Answer 1

This problem is related to finding the real roots of equation ax²+bx+c=0. If b²-4ac>0, then equation has two distinct roots x₁, x₂ and factorization is expressed by ax²+bx+c=a(x-x₁)(x- x₂). If b²-4ac=0, then equation has two equal roots
x₁= x₂ =z and factorization is expressed by ax²+bx+c=a(x-z)². If b²-4ac<0, then equation has no real roots and it is impossible to factor trinomial ax²+bx+c.