Fast Please answer Algebra 2
How do I do.
Find a quadratic equation with integral coefficients having the given roots.
1+ √3, 1 - √3

Question

Fast Please answer Algebra 2
How do I do.
Find a quadratic equation with integral coefficients having the given roots.
1+ √3, 1 - √3

anonymous · Answer

I got a[x^2-2x-2=0
is that correct?

agent0smith · Answer

If a quadratic has roots a and b, you can write it as (x - a)(x - b)

Your roots are (1+ √3) and (1 - √3) so you just have to enter those in place of a and b (and FOIL/expand if necessary) and that should satisfy the question.

anonymous · Answer

so can i skip the step of a[x^2- (sum of roots)x + (product of roots)]=0 step?

anonymous · Answer

or is it the same thing as (x-a)(x-b) but written diffrently?

agent0smith · Answer

You could probably do it that way too... should work.

anonymous · Answer

they are correct. or the back of the back says so.

agent0smith · Answer

Yeah, my mistake, they are.

anonymous · Answer

one quick question, does (x-b)(x-a) always work?

agent0smith · Answer

Yes, it should. That's where the roots come from. 
$$ax^2-2x-2 $$looks good to me.

agent0smith · Answer

Even if the roots are complex numbers, you can put them into (x-b)(x-a)

anonymous · Answer

As 2times 3 = 3times2,
(x-a)(x-b) = (x-b)(x-a)