Find a polynomial equation f(x)=0 satisfying the given conditions. Degree 4; the coefficients are integers; 1/2 is a root multiplicity two; 3x^2-2x-1 is a factor of f(x)

Question

f(x)=

Answer 1

Root multiplicity of 2 means

(2x -1)(2x-1)

where the roots are 1/2 for each term.

You can then multiple the 3x²-2x-1 by these two terms to expand and get a polynomial of degree 4.

(2x -1)(2x-1)(3x²-2x-1)