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

Question

amistre64 · Answer

$$\pm\frac{factors.of. a_n}{factors.of. a_0}$$
rational root thrm

amistre64 · Answer

if these dont work, it gets messy

amistre64 · Answer

might have to resort to fancier trial and error methods

anonymous · Answer

Ohh, rational root theorem. hmm can you explain it a lil'bit. How does it work and stuff.

anonymous · Answer

okay. so, it doesn't works always.

anonymous · Answer

How about if $p(x) = x^2+12x-5$?

amistre64 · Answer

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 · Answer

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 · Answer

otherwise, for quadratics, we can use the quadratic formula, which is just the shorthand version of completeing the square