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miley23
 2 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, 13, and 5 + 4i
A. f(x) = x4  8x3  12x2 + 400x  1599
B. f(x) = x4  200x2 + 800x  1599
C. f(x) = x4  98x2 + 800x  1599
D. f(x) = x4  8x3 + 12x2  400x + 1599
miley23
 2 years ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, 13, and 5 + 4i A. f(x) = x4  8x3  12x2 + 400x  1599 B. f(x) = x4  200x2 + 800x  1599 C. f(x) = x4  98x2 + 800x  1599 D. f(x) = x4  8x3 + 12x2  400x + 1599

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ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0Remember, to have zeros 3, 13 and 5+4i, f has factors x3, x+13 and x5+14i. Also if 5+4i is a zero, then 54i is also a zero. So at least f should look like: f(x)=(x3)(x+13)(x5+14i)(x514i). Now all you have to do is expand f to see which of A,B,C or D it is!

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0TYPO: read 4i and 4i instead of 14i ;)

ZeHanz
 2 years ago
Best ResponseYou've already chosen the best response.0http://www.wolframalpha.com/input/?i=expand+%28x3%29%28x%2B13%29%28x5%2B4i%29%28x54i%29

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0this part \((x(5+4i))(x(54i))\) can be a bit tricky. there are several ways to do it

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0one way is to work backwards: \[x=5+4i\] \[x5=4i\] \[(x5)^2=16\] \[x^210x+25=16\] \[x^210x+41\] is the quadratic

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0another way to to memorize that if the zeros are \(a+bi\) and \(abi\) then the quadratic with those zeros is \(x^22ax+a^2+b^2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0you can then go right to \((x(5+4i))(x(54i))=x^210x+5^2+4^2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.0of course another way it to type it in to wolfram
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