Question

1: Find the equation of a polynomial with given zeros

Answer 1

For this problem, we are given the zeros of a polynomial, we need to determine its expression.

The zeros are:

`1,1,2+√(2),2-√(2)`

Therefore we can write:

`\begin{gathered} f(x)=(x-1)^2(x-2+√(2))(x-2-√(2))\\ \\ f(x)=(x^2-2x+1)(x^2-4x+2)\\ \\ f(x)=x^4-4x^3+2x^2-2x^3+8x^2-4x+x^2-4x+2\\ \\ f(x)=x^4-6x^3+11x^2-8x+2 \end{gathered}`

The correct answer is option A.