1-√3,1 + √3 - 2   find polynomial function of degree with given numbers as zeros

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let x1 and x2 be the roots such that:

x1= 1- sqrt3

x2= 1+sqrt3

Then ( x-x1) and (x-x2) are factors of the function :

==> f(x) = [x - (1-sqrt3)] [ x - (1+sqrt3)]

              = (x -1 + sqrt3) (x-1 - sqrt3)

Now let us expand the brackets:

             ...

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let x1 and x2 be the roots such that:

x1= 1- sqrt3

x2= 1+sqrt3

Then ( x-x1) and (x-x2) are factors of the function :

==> f(x) = [x - (1-sqrt3)] [ x - (1+sqrt3)]

              = (x -1 + sqrt3) (x-1 - sqrt3)

Now let us expand the brackets:

              = x^2 - x - sqrt3*x - x + 1 + sqrt3 + sqrt3*x - sqrt3 - 3

Reduce and group similar terms:

              = x^2 - 2x - 2

==> f(x)= x^2 - 2x -2

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