Find the polynomial fx of lowest degree with real coefficien

Find the polynomial f(x) of lowest degree with real coefficients and having the zeros 4 + Squareroot 2. 4- Squareroot2, and 4 Choose the correct polynomial of lowest degree with only real coefficients and having the zeos f(x) = x^4 5x^3-9x^2 + 9x+8 f(x) = x^3-8x^2+5x-3 f(x)=x^3- 12x^2 + 46x- 56 f(x)-3x^3+ 3x^2-8x-8

Solution

zeros are 4 +sqrt(2

0 , 4-sqrt(2) and 4

so f(x) = (x - (4+sqrt(2) ) . (x - (4-sqrt(2)) . (x-4)

= (x^2 -4x +xsqrt(2) -4x -xsqrt(2) -2 +16) (x-4)

=(x^2 -8x +14)(x-4)

=(x^3 -12x^2 +46x -46

option c). is correct answer