Finding solutions to a quadratic equation by factoring
Posted on 2003-03-13
I'm going over my algebra so I can finally go to college. There's this one issue that I never really understood back in high-school:
When you have an quadratic equation, we were taught that you can solve it by using factoring.
My problem is that to factor, the book I have just tells you to *guess* two numbers that add up to equal x and multiply to equal y.
x*x - 11x + 28 = 0
can be converted to:
(x-4)(x-7) = 0
where you can solve it easily.
Isn't there a better way than guessing them? What would you do with seven-digit or non-integer numbers?
(When I tried solving the set of equations of:
m * n = 28
m + n = -11
I just got back to the original quadratic function- just with the m instead of x)
Don't mathematicians have a better method to do this? Math just always seemed the last place where guessing is the way to solve problems.