Let p(x) be a quadratic polynomial with integer coefficients which has 4 - sqrt(17) as a root. Compute p(3)/p(4).
p(x) = ax^2 + bx + c
The roots are 4 + sqrt 17 and 4 - sqrt 17
By Vieta
sum of the roots = 8 = -b/a = -b/1 ⇒ b = -8
product of the roots = 16 - 17 = -1 = c /a = c /1 ⇒ c = -1
p(x) = x^2 -8x - 1
p(3) / p(4) = -16 / -17 = 16 / 17
