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## Ishaan94 3 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

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

2. amistre64

if these dont work, it gets messy

3. amistre64

might have to resort to fancier trial and error methods

4. Ishaan94

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

5. Ishaan94

okay. so, it doesn't works always.

6. Ishaan94

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

7. 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

8. 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

9. amistre64

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

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