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aga3t
 one year ago
Using the given zero, find all other zeros of f(x).
2i is a zero of f(x) = x^4  45x^2  196
aga3t
 one year 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
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1roots are 7,7,2i, 2i

cwrw238
 one year 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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