Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −1, 1, square root 3 ; integer coefficients and constant term 6

Answer 1

If √3 is a root, so is -√3; thus, the polynomial is c(x-1)(x+1)(x-√3)(x+√3) = c(x²-1)(x²-3) = c(x⁴-4x²+3)

As the constant term is 6, 3c = 6, so c = 2

2(x⁴-4x²+3) = 2x⁴-8x²+6