Let p(x) be a quadratic polynomial with integer coefficients which has 3+sqrt7 as a root. Compute p(2)/p(3).
+36916 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 !
