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aga3t

  • 2 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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  1. cwrw238
    • 2 years ago
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    +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

  2. cwrw238
    • 2 years ago
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    roots are 7,-7,-2i, 2i

  3. cwrw238
    • 2 years ago
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    i 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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