Write a polynomial function $f$ of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form

Question

Given zeros are -6,0,3 (negative square root) of 5

Answer 1

(x+6)(x)(x-3)(x^2+5)

multiply those factors to get a 5th degree polynomial, starts with x^5, ends with no constant term. ends with an x term: -90x. also x^4, x^3 and x^2 terms with coefficients each, found when you multiply out the 5 factors

there's a 5th zero not listed, the conjugate of -sqr(-5): +sqr(-5) imaginary zeroes always come in conjugate pairs

x^5 +3x^4 -13x^3 + 15x^2 -90x