How do you solve quadratic functions when a value is not 1 or -1. For example: 2x^2 -10x+7=0

Question

mathstudent55 · Answer

Here you have a = 2, b = -10, c = 7
Plug them in the quadratic formula and see what you get.

anonymous · Answer

I remember learning a way to solve "tricky trinomials" in class, something about multiplying a and c and finding roots of b, maybe? I don't know.

mathstudent55 · Answer

For ax^2 + bx + c, that is a way of factoring a trinomial. Multiply a and c together, then come up with two factors of ac that add up to b. Let's call these two factors p and q. Then break up the middle term into two terms with the new numbers as coefficients px and qx, and factor by parts. ax^2 + px + qx + c factor by parts. That means take a factor out of the first two terms and take a factor out of the last two terms.

anonymous · Answer

Thanks so much! But in myu question, A and C multiply to 14, but neither 14 and 1 or 7 and 2 add to 8, so what do I do in this case?

anonymous · Answer

awkward... by 8 I mean 10, but either way, it doesn't work out.

mathstudent55 · Answer

If there are no factors of ac that add up to b, then that means it's not factorable, and you need to use the quadratic formula.

mathstudent55 · Answer

For example, factor 12x^2 - 23x + 10
Multiply ac: ac = 120
What are two factors of ac that add up to 120? 15 and 8
12x^2 - 15x - 8x + 10 =
3x(4x - 5) - 2(4x - 5) =
(4x - 5)(3x - 2)

anonymous · Answer

okay, I'll try that, Thanks! You are really cool!

mathstudent55 · Answer

In this example, 120 does have factors that add up tp -23. Actuall the factors were -15 and -8, not 15 and 8.

mathstudent55 · Answer

You're welcome.