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anonymous
 one year ago
Write a polynomial with rational coefficients having roots 3, 3+i, and 3i.
Part 1: Write the factors (in the form xa) that are associated with the roots (a) given in the problem.
Part 2: Multiply the 2 factors with complex terms to produce a quadratic expression.
Part 3: Multiply the quadratic expression you just found by the 1 remaining factor to find the resulting cubic polynomial.
anonymous
 one year ago
Write a polynomial with rational coefficients having roots 3, 3+i, and 3i. Part 1: Write the factors (in the form xa) that are associated with the roots (a) given in the problem. Part 2: Multiply the 2 factors with complex terms to produce a quadratic expression. Part 3: Multiply the quadratic expression you just found by the 1 remaining factor to find the resulting cubic polynomial.

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(x(3+i))(x(3i))\] is a pain to multiply there is a much easier wy

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you want a quadratic with zeros \(3+i\) and \(3i\) there is an easy way to find it also a real real easy way which would you like to use?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well 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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what difference does it make? you have to end up with a quadratic, might as well just write it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if the zeros are \(a\pm bi\) the quardratic is \[x^22ax+(a^2+b^2)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok then lets multiply

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So how do I find my factors for this problem?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if a root is \(r\) then a factor is \((xr)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0your roots are 3, 3 + i, 3  i so your factors are \[(x3)(x(3+i))(x(3i))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay yes that's what I got

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is the answer to A

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for B they want you to multiply \[(x(3+i))(x(3i))\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the complex roots only? I see.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that is what is says right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do I multiply this by FOIL?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well ok i guess, but keep \(3+i\) and \(3i\) together lets do the first outer inner last business, but to it the easy way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so don't distribute the x to the roots?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first is a no brainer, it is \(x^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets skip to the last when you multiply a complex number \(a+bi\) by its complex conjugate \(abi\) you get the real number \(a^2+b^2\) to the "last" is \[3^2+1^2=10\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh okay I've never seen that before.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then "outer and inner"\[(3+i)x(3i)x\]combine like terms, the \(i\) part goes bye bye and you are left with \(6x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So did you distribute the x first, then subtract?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you haven't seen that then you should learn it now \[(a+bi)(abi)=a^2+abiabib^2i^2=a^2+b^2\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i would call it "distribute then combine like terms" but it is the same thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Okay thanks. Okay and so the last part is to multiply the quadratic we found by x3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0final answer \[x^26x+10\] as promised

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i will let you do that yourself, it is easy enough right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah it'll take me a while because I'm rusty but I can do it. Thank you so much!
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