SOLUTION: Find a fourth degree polynomial equation with integer coefficients that has the given numbers as roots. 3 + square root of 2 and the square root of 5

Question 218695: Find a fourth degree polynomial equation with integer coefficients that has the given numbers as roots.
3 + square root of 2 and the square root of 5

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find a fourth degree polynomial equation with integer coefficients that has the given numbers as roots.
3 + square root of 2 and the square root of 5
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f(x) = (x-(3+sqrt(2))(x-(3-sqrt(2))(x-sqrt(5))(x-(-sqrt(5))
---------------------------------------------------------------
Modify the factors:
f(x) = ((x-3)-sqrt(2))((x-3)+sqrt(2))(x-sqrt(5)(x+sqrt(5)
---
f(x) = [(x-3)^2-2][x^2-5]
f(x) = [x^2-6x+7][x^2-5]
==============================
Cheers,
Stan H.
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