Question

Why is 'b' in ax2 + bx + c not the sum of the factors of c?

Answer 1

You mean,

if m and n are factors, then ax2 + bx + c = (x-m)(x-n)

Then why is isn't a+c=b?

Answer 2

Because b has an x term.

Answer 3

That is why isn't m+n=b?

Answer 4

Oh okay. Thanks, you guys.

Answer 5

Your welcome @MaydayParadeee :)

Answer 6

a) When a = 1, quadratic equation x^2 + bx + c = 0, Any factor pair of c whose sum equals to (-b) is the real root pair. If you can't find such a factor pair, the quadratic equation can't be factored, then use the formula to solve it.
b) When a is not 1: quadratic equation in standard form: ax^2 + bx + c = 0. The 2 real roots are usually in the form of 2 fractions. Their product is (c/a) and their sum is (-b/a). There is a new method called "the Diagonal Sum Method" that creates a rule. Given a pair of 2 real roots (c1/a1) and (c2/a2). Its diagonal sum is : (c1a2 + c2a1). The method's rule is: If a factor pair of (c/a) has its diagonal sum equals to (-b), this pair is a real root pair.
This above paragraph intends to let you know the relationship between a, b, and c in a quadratic equation.