anonymous one year ago Factor x2 - 2x + 3

1. aric200

Do you mean Factor x^2 - 2x + 3

2. UsukiDoll

@aric200 yes that's got to be the equation

3. UsukiDoll

anyway , to factor we focus on the middle term and the last term first then the sign patterns of the equation

4. anonymous

@aric200 yes sir

5. UsukiDoll

so the last term we have is a 3 and there is only one combination which is 1 x 3 = 3 so now let's grab the middle term. We notice that there is a -2 so our 1 must be positive and our 3 must be negative 1-3 = -2

6. aric200

It bothers me when people do not put the ^Carrots.

7. UsukiDoll

or am I reading this too fast? wait... I'm using discriminant formula

8. UsukiDoll

(-2)^2-4(1)(3) 4-12 = -8 oh nice.. we can't factor this -_- quadratic formula time

9. UsukiDoll

$\frac{-b \pm \sqrt{b^2-4ac} }{2a}$

10. UsukiDoll

so with the discriminant formula we already figured out the square root portion which was -8, so we let a = 1 b = -2 and c = 3 because our equation $x^2-2x+3$ in the form of the standard quadratic equation which is $ax^2+bx+c$

11. UsukiDoll

now we just plug in our data $\frac{2 \pm \sqrt{-8} }{2}$

12. UsukiDoll

but we are not done... we can split that 8 up and negatives aren't allowed in the radicals which means we are going to get an imaginary or i out of this

13. UsukiDoll

$\frac{2 \pm 2\sqrt{2}i }{2}$

14. UsukiDoll

now we can get split this up and get rid of the 2's

15. UsukiDoll

$\frac{2+2 \sqrt{2}i}{2}, \frac{2-2 \sqrt{2}i}{2}$

16. UsukiDoll

$1+\sqrt{2}i, 1-\sqrt{2}i$

17. UsukiDoll

which is our roots..

18. anonymous

@UsukiDoll so thats it?!

19. UsukiDoll

I think it should look like this? not sure $(x-(1+\sqrt{2}i))(x-(1-\sqrt{2}i) )$

20. UsukiDoll

@ganeshie8 I'm missing something in here...aren't I?

21. UsukiDoll

it's just that when I use to do those problems, all of my professors care about are the roots and I didn't have to put it back into factored form like what I just typed.

22. ganeshie8

yeah the given quadratic cannot be factored over integers, it is prime