anonymous
  • anonymous
Given a Polynomial, \(p(x) = a_0 + a_1x^2 + \ldots +a_nx^n\). How would I get number of real roots for \(p(x)=0\)?
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
\[\pm\frac{factors.of. a_n}{factors.of. a_0}\] rational root thrm
amistre64
  • amistre64
if these dont work, it gets messy
amistre64
  • amistre64
might have to resort to fancier trial and error methods

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anonymous
  • anonymous
Ohh, rational root theorem. hmm can you explain it a lil'bit. How does it work and stuff.
anonymous
  • anonymous
okay. so, it doesn't works always.
anonymous
  • anonymous
How about if \(p(x) = x^2+12x-5\)?
amistre64
  • amistre64
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
amistre64
  • amistre64
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
amistre64
  • amistre64
otherwise, for quadratics, we can use the quadratic formula, which is just the shorthand version of completeing the square

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