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anonymous
 one year ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, 2, and 1 + 2i
here are my choices
f(x) = x^4  7x^2  26x  40
f(x) = x^4  3x^3  8x^2  13x  40
f(x) = x^4 + 6.5x^2  26x  40
f(x) = x^4  3x^3 + 8x^2 + 13x + 40
anonymous
 one year ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 4, 2, and 1 + 2i here are my choices f(x) = x^4  7x^2  26x  40 f(x) = x^4  3x^3  8x^2  13x  40 f(x) = x^4 + 6.5x^2  26x  40 f(x) = x^4  3x^3 + 8x^2 + 13x + 40

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont know how to do this at all lolol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok then we better go slow

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know if \(r\) is a zero, then one factor must be \((xr)\)? so in this case you have \(4\) is a zero making one factor \((x4)\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0clear or not? that is really what we need to start this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh okay so (x4) and (x+2) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we start with \[(x4)(x+2)\] now we have more work to do

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you also need the quadratic that has the zeros of \(1+2i\) and it "conjugate" \(12i\) next job is to find that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0any ideas? "no" is a fine answer

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok there is a hard way, an easy way, and a really really easy way lets do the easy way first, then the real easy way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0work backwards starting with \[x=1+2i\] add \(1\) to get \[x+1=2i\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then square both sides (carefully) to get \[(x+1)^2=(2i)^2\] or \[x^2+2x+1=4\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0add 4 to both sides to finish with \[x^2+2x+5\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0final job is to multiply \[(x4)(x+2)(x^2+2x+5)\]i would cheat so as not to screw up the algebra

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=%28x4%29%28x%2B2%29%28x^2%2B2x%2B5%29

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and would that be the answer? or is there more

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0OOO got it. thank you
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