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nah don' t do that
\[(x-(3+i))(x-(3-i))\] is a pain to multiply there is a much easier wy
you want a quadratic with zeros \(3+i\) and \(3-i\) there is an easy way to find it also a real real easy way which would you like to use?
Well I am pretty sure I can find the easier way, but the packet I'm doing requires me to do it the hard way, unfortunately. Can you help me with the harder way?
what difference does it make? you have to end up with a quadratic, might as well just write it
Well each of the steps is graded separately as a different question. So if I skip the first two steps (or do them differently) then I get points taken off.
if the zeros are \(a\pm bi\) the quardratic is \[x^2-2ax+(a^2+b^2)\]
ok then lets multiply
So how do I find my factors for this problem?
if a root is \(r\) then a factor is \((x-r)\)
your roots are 3, 3 + i, 3 - i so your factors are \[(x-3)(x-(3+i))(x-(3-i))\]
Okay yes that's what I got
that is the answer to A
for B they want you to multiply \[(x-(3+i))(x-(3-i))\]
So the complex roots only? I see.
that is what is says right?
Do I multiply this by FOIL?
well ok i guess, but keep \(3+i\) and \(3-i\) together lets do the first outer inner last business, but to it the easy way
so don't distribute the x to the roots?
first is a no brainer, it is \(x^2\)
lets skip to the last when you multiply a complex number \(a+bi\) by its complex conjugate \(a-bi\) you get the real number \(a^2+b^2\) to the "last" is \[3^2+1^2=10\]
Oh okay I've never seen that before.
then "outer and inner"\[-(3+i)x-(3-i)x\]combine like terms, the \(i\) part goes bye bye and you are left with \(-6x\)
So did you distribute the x first, then subtract?
if you haven't seen that then you should learn it now \[(a+bi)(a-bi)=a^2+abi-abi-b^2i^2=a^2+b^2\]
yes i would call it "distribute then combine like terms" but it is the same thing
Okay thanks. Okay and so the last part is to multiply the quadratic we found by x-3?
final answer \[x^2-6x+10\] as promised
yes i will let you do that yourself, it is easy enough right?
Yeah it'll take me a while because I'm rusty but I can do it. Thank you so much!