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anonymous

  • 5 years ago

find all the zeros for f(x)=x^4-4x^3+x^2+8x-6

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  1. anonymous
    • 5 years ago
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    Found one!

  2. anonymous
    • 5 years ago
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    (Try out the obvious numbers for some roots, then factorise the rest) Note that if f(a) = 0, then (x-a) is a factor.

  3. anonymous
    • 5 years ago
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    I found 3, is there more and how do I solve this?

  4. anonymous
    • 5 years ago
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    f(3) = 0, yes. So you can write f(x) (x-3)(ax^3 + bx^2 + cx +d) And reduce it to a cubic. However there is one more (even easier!) factor you should be able to spot first. That will reduce it to a qudratic which you can formularise.

  5. anonymous
    • 5 years ago
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    the number 1

  6. anonymous
    • 5 years ago
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    Indeed. => f(x) = (x-1)(x-3)(ax^2+bx+c) Hint, once you find the last factor (quadratic) it will reduce no more so you'll need to use the formula or similar (or maybe common sense, once you see what it is).

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