Thread: quadratic formula

Hi all,

I wanted to ask what is the method of simpliflying a quadratic equation without using the formula method. This is probably a easy question but I always get confused and end up using the formula instead, where other people can do it in their head. (like for a non-calculator paper you can't really rely on the formula)

As I learnt the foil method 2 weeks ago from the MHF, a way for expanding brackets which i find very useful.

Lets take an example of: x^2 -8x + 15

Thanks

Originally Posted by dadon

Hi all,

I wanted to ask what is the method of simpliflying a quadratic equation without using the formula method. This is probably a easy question but I always get confused and end up using the formula instead, where other people can do it in their head. (like for a non-calculator paper you can't really rely on the formula)

As I learnt the foil method 2 weeks ago from the MHF, a way for expanding brackets which i find very useful.

Lets take an example of: x^2 -8x + 15

Thanks

I'm assuming you're trying to find the solutions to:

x^2 - 8x + 15 = 0

Factor it: (x - 5)*(x - 3)

Factoring takes time to learn, and after a while you can just see it. You try find two numbers that will sum to 8 (-5x + (-3x)) and whose multiple is 15 (which we have (-5)*(-3) = 15). The x's are standard, since we have x^2 and we know it will be (x ...)*(x ...).

Of course, you could just use the quadratic formula, but you wanted to know this way instead.

So, we have:

(x - 5)*(x - 3) = 0

And thus,

(x - 5) = 0 ^ (x - 3) = 0,

So, x = 5 or x = 3