What represents the solutions of a quadratic equation?

Answer 1

A quadratic equation is one that can be written as y=Ax^2+Bx+C. The solutions are the values of x that make y=0. If an equation has solutions, say x=M and x=N, then Ax^2+Bx+C=(x-M)(x-N).

For example:

y=x^2-5x+6

So we want to find what values of x make the equation true:

0=x^2-5x+6

This happens at x=2, when

y=(2)^2-5*(2)+6

=4-10+6

=0

and at x=3, when

y=(3)^2-5*(3)+6

=9-15+6

=0

So the solutions are x=2 and x=3, and the equation can be written as y=(x-2)(x-3).