Write a polynomial function with integral coefficients with zeros -3, 2, and -i square root 6.

Answer 1

One trick that's useful to know is that for polynomials with real coefficients, any complex roots come in pairs. So, if -isqrt(6) is a root, so is +isqrt(6).

So, one such polynomial would be:

(x+3)*(x-2)*(x+isqrt(6))*(x-isqrt(6))

=(x+3)*(x-2)*(x^2+6)

=(x+3)*(x^3-2x^2+6x-12)

=x^4+x^3+6x-36.

Answer 2

zeros are -3, 2, -isqr6 and +isqr6. imaginary zeros come in conjugate pairs

to find the factors change the sign and stick an x in front

(x+3)(x-2)(x+isqr6)(x-isqr6)

= (x^2+x-6)(x^2 + 6)

= x^4 +x^3 +6x -36