How do you write the polynomial function with the least degree and zeroes 1, 4, 1 + √2?

1 Answer
Mar 5, 2016

Answer:

#x^3-(6+sqrt2)x^2+(9+5sqrt2)x-4(1+sqrt2)#

Explanation:

A polynomial function with the least degree and zeroes #{1, 4, (1 + sqrt2)}# will be given by

#(x-1)(x-4)(x-(1+sqrt2))# or

#(x-1-sqrt2)[x(x-4)-1(x-4)]# or

#(x-1-sqrt2)(x^2-4x-x+4)# or #(x-1-sqrt2)(x^2-5x+4)# or

#x(x^2-5x+4)-1(x^2-5x+4)-sqrt2(x^2-5x+4)# or

#x^3-5x^2+4x-x^2+5x-4-sqrt2x^2+5sqrt2x-4sqrt2# or

#x^3-(6+sqrt2)x^2+(9+5sqrt2)x-4(1+sqrt2)#