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anonymous
 3 years ago
Using the given zero, find all other zeros of f(x).
2i is a zero of f(x) = x^4  45x^2  196
anonymous
 3 years ago
Using the given zero, find all other zeros of f(x). 2i is a zero of f(x) = x^4  45x^2  196

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cwrw238
 3 years ago
Best ResponseYou've already chosen the best response.1+2i is also a solution dividing 4 into 196 gives 49 so it looks like 7 and 7 may be roots plugging these values gives 7^4  45*49  196 = 0

cwrw238
 3 years ago
Best ResponseYou've already chosen the best response.1i ought to explain some more about the above; complex roots exist as pairs if a + bi is a root then the other is a  bi thats why +2i is another root of your equation to find the other roots i used the rational root theorem the factors of 196 are +/1, +/ 2, +/4, +/7, +/14, +/28, +/ 49 and are possible roots i was lucky that i guessed it might be +7 and 7 first an equation in x^4 will have 4 roots , if some are complex there will be 2 of them
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