How do you write a polynomial function given the real zeroes 8,-i, i and coefficient 1?

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Answer 1 · 2015-11-28T18:41:52

For each zero c, meaning f(c) = 0, your function f(x) has to have a factor (x - c). Your function needs ___ factors. (You fill in!)

Concept: If $x = c,$ $x = c,$ then $x - c = 0$ $x - c = 0$ . We want $f (c) = 0 .$ $f(c) = 0.$

We have zeroes: $x = ?, x = ?, and x = ? .$ $x = ?, x=? ,and x=?.$

So we will have factors: $(x - ?), (x - ?), and (x - ?) .$ $(x - ?), (x - ?), and (x-?).$

$f (x)$ $f(x)$ needs all these factors, so

$f (x) = (x - ?) (x - ?) (x - ?)$ $f(x) = (x-?)(x-?)(x-?)$ . Now multiply it out!

Does this have the right (leading) coefficient?

You'll learn more if you finish this yourself!
(shortcut: use difference of squares!)

...//dansmath strikes again! \\...