Question

Trying to setup quadratic equation, but not clear on multiplying these two roots together, I'm not sure if I clear the fractions or just multiply with the fractions?
(x-(1/2 + 1/4 Sqrt5))(x-(1/2 -1/4 Sqrt5))
What I am starting with is..
(x-(3/4 Sqrt5)(x-(1/4 Sqrt5) ? any ideas?

Answer 1

your case is the first one:\[(x-a)(x-b) = x^2 - (a+b)x + ab\]\[(x+a)(x+b) = x^2 + (a+b)x + ab\]\[(x+a)(x-b) = x^2 + (a-b)x - ab\]

Answer 2

your ab will look like (y + zsqrt(5))

no need to simplify fractions before expanding brackets

Answer 3

actually there won't be sqrt(5) in ab since they end up canceling out

Answer 4

I'm not sure I follow?

Answer 5

So how would they cancel out?

Answer 6

by adding/multiplying.

i did it on paper, scanning it and uploading it ^_^

Answer 7

ok. great

Answer 8

i followed my "formula" which is what you'd get by doing FOIL.

it avoids a few steps though

let me know if you have questions

http://img199.imageshack.us/img199/7948/gedd.jpg

Answer 9

ok. well that seems to work out, I don't know what the answer is supposed to be, but it makes sense. It's a little weird to see it worked out this way. but thank you very much. It'll take me a minute to really understand this.
Thank you

Answer 10

no problem ^_^

to confirm answers, this site is great: http://www.wolframalpha.com/input/?i=%28x-%281%2F2+%2B+1%2F4+Sqrt5%29%29%28x-%281%2F2+-1%2F4+Sqrt5%29%29&dataset=

Answer 11

you'll wanna scroll down to "alternate forms"

Answer 12

\[[x-(1+\sqrt{2i})/3][x-(1-\sqrt{2i)/3]}\]

Answer 13

its pretty unclear what the fraction is:

\[\frac{ 1 \pm \sqrt{2i} }{ 3 }\] or\[1 \pm \frac{ \sqrt{2i} }{ 3 }\]

Answer 14

oh yes. sorry its the first example you wrote

Answer 15

do I have to multiply by 3 to clear the fraction?

Answer 16

nope. you can always just add/multiply fractions

Answer 17

so I would get x^2-1/3+sqrt2i/3-1/3-sqrt2i/3?

Answer 18

yes

Answer 19

let me know if you have questions. sorry for scribble at bottom. ignore the FOIL thing if you already know about it. i can improve my explanation of it but i think you might already know about it:

http://img818.imageshack.us/img818/7726/7hvn.jpg

Answer 20

thank you for your help. I really appreciate it.