Question

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

−b
b^2 − 4ac
2a

I thought it would be b^2 − 4ac because that's the most part of the formula, but this question confused me.

Answer 1

You are correct, to understand it a little better, \(b^2-4ac\) is known as the discriminant. Solving it will give you one of three cases \[b^2-4ac > 0\] \[b^2-4ac = 0\] and \[b^2-4ac< 0.\] When > 0, the solution will have two real roots, when = 0 the solution with have two real roots that are equal to one another, thus there will be one distinct root, and when <0 there will be no real solutions to the equation. With that said, to answer your question, factoring works only when using integers, thus when the discriminant is \( \ge 0\), the equation can be factored.

Answer 2

Hope that helped

Answer 3

Thanks, that really helped :)