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Rational Zeros Theorem Proof

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Text Comments (19)
Nick B (3 months ago)
When you claim that -a0q^n is divisible by P, how are you sure that the the expression to the right of P is an integer? 2*4.5 = 3*3 but 2 does not divide 3 for example. This part was confusing.
Phoenix Fire (9 days ago)
+What the Hectagon?! I meant it as multiply by the largest denominator in the coefficients, get a new polynomial, multiply by the new largest denominator in the coefficients, etc.. This is equivalent to multiplying by the least common denominator. I normally do it this way to avoid having to prime decompose every denominator. Still though, you're right. My way isn't standard, and I didn't explain it in enough detail when I brought it up. In the end, it is needlessly confusing and unhelpful. Thank you for catching me on that.
What the Hectagon?! (9 days ago)
+Phoenix Fire Slight correction, you said "largest denominator," when I think you mean common denominator. Obviously the easiest to use would be the LEAST common denominator, but simply multiplying by the largest denominator in all the coefficients won't do in general (say all of them are different primes, for example). Otherwise, good explanation.
Phoenix Fire (11 days ago)
That's a fair point. The truth is that this method for finding solutions was developed only for polynomials with integer coefficients. Since this method also only looks for rational solutions, p and q are integers by definition. If you have rational coefficients, just multiply the entire polynomial by the largest denominator and repeat until you get a polynomial with integer coefficients. Since multiplying your entire polynomial by a constant doesn't change the solutions, this gets you the same solutions. I don't know of any way to get the rational solution of a polynomial with general real or complex coefficients.
Ultradodgykid (1 month ago)
Nick B but 4.5 isnt an integer, the coeffs of the polynomial are all integers
crihs (7 months ago)
Very well explain.
Om Patel (7 months ago)
Thanks man
sabra ansari (10 months ago)
Thank you sir.
Fatima Khoogar (11 months ago)
Thanks, It was really helpful
chen adam (1 year ago)
Because this is an equation and Q is a factor on the left-hand side it must be a factor on the right-hand side and because P over Q is the lowest term so there's no common factor, it must be a factor of asubn which means a sub n can have Q as one of its factors. do I get it right?
Fatima Khoogar (2 years ago)
thanks, very helpful and simply explained
Kate Yen (2 years ago)
Thanks a lot>>.;))
Hikari Tanaka (3 years ago)
Thank you so so much! This was so easy to understand!!!!
ashuk206 (3 years ago)
Nooooo, I'm so close to fully understanding this. I get that p has to be a factor of asub0 and q has to be a factor of asubn, but I don't get why they have to be integers. By your logic,couldn't we also pull out a half from 10 and that counts as a factor?
Æryn Meader (2 years ago)
p and q must be integers since p/q has to be a fraction in lowest terms.
Kenny Duran (4 years ago)
Oh my goodness, thank you so much! I'm just learning a bit of algebra ii and I didn't want to use an equation I had no understanding of. This helps a lot!
ONEEZE (4 years ago)
Yea knowing this cuts down on having to remember a lot of things. This way the rules present themselves without much memory.
Thaddaeus Rhone (4 years ago)
Thanks buddy.
ONEEZE (4 years ago)
No Problem.

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