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Let p(x) be a quadratic polynomial with integer coefficients which has 3+sqrt7 as a root. Compute p(2)/p(3).

 Jul 22, 2019
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The other root of the quadratic will be the conjugat of the given root...your polynomila will look like this:

 

(x - (3 + sqrt 7)) * (x-(3-sqrt 7))

= x^2    - 3x  + x sqrt 7     -3x    +9  - 3 sqrt 7  - sqrt 7x + 3 sqrt 7 - 7

= x^2 -6x +2         Now I think YOU can put in x = 2    to find the value in the numerator of your question

                               then put in x = 3 for the denominator.....   Let me know what you find !

 Jul 22, 2019

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