Practice!

Sample Problem

Find a polynomial function that has zeroes at x=1+√2, 1-√2, and 1

Solution

If the function has zeroes at x=1+√2, 1-√2, and 1, the function (with least multiplicity, that is) could look like this:

f(x)=(x-(1+√2))(x-(1-√2))(x-1)=0

f(x)=(x2-2x-1)(x-1)

f(x)= x3-3x2+x+1