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Ishaan94

  • 2 years ago

Given a Polynomial, \(p(x) = a_0 + a_1x^2 + \ldots +a_nx^n\). How would I get number of real roots for \(p(x)=0\)?

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  1. amistre64
    • 2 years ago
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    \[\pm\frac{factors.of. a_n}{factors.of. a_0}\] rational root thrm

  2. amistre64
    • 2 years ago
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    if these dont work, it gets messy

  3. amistre64
    • 2 years ago
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    might have to resort to fancier trial and error methods

  4. Ishaan94
    • 2 years ago
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    Ohh, rational root theorem. hmm can you explain it a lil'bit. How does it work and stuff.

  5. Ishaan94
    • 2 years ago
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    okay. so, it doesn't works always.

  6. Ishaan94
    • 2 years ago
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    How about if \(p(x) = x^2+12x-5\)?

  7. amistre64
    • 2 years ago
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    your poly is backwards so my write up is upside down i think the idea is that the last term needs to have a factor of a0/an .. in this case to even have a shot of working out

  8. amistre64
    • 2 years ago
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    what are the rational roots of 5/1 ? 1,5,-1,-5 if these are gonna be roots, they will create a 0 when plugged into the equation

  9. amistre64
    • 2 years ago
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    otherwise, for quadratics, we can use the quadratic formula, which is just the shorthand version of completeing the square

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