Form a quadratic polynomial whose zeroes are 3 - sqrt(3)/5 and 3 + sqrt(3)/5.
+128475 Let the quadratic be of the form ax^2 + bx + c
Let us suppose that the quadratic is monic ( a =1)
By Vieta....
The sum of the roots = -b = (3 + sqrt 3) / 5 + ( 3 - sqrt 3) / 5 = 3/5 + 3/5 = 6/5
So b = -6/5
And the product of the roots = c = (3 + sqrt 3) / 5 * (3 - sqrt 3) / 5 = [ 9 - 3 ] /25 = 6/25
So....the monic polynomial is
x^2 - (6/5)x + ( 6 / 25 )
If we wanted integer coefficients we also could have
25x^2 - 30x + 6 ....... many other answers are also possible
