Write an equation in standard form for the polynomial with given zeros x=-1, x=4i, and x=√6. Show your work.

Question

You may leave equation in factored form, but it must have real number coefficients. Assume a=1

Answer 1

x+1 is one factor

x=4i

x^2 =-16

x^2+16 is another factor

x = sqr6

x^2 = 6

x^2 -6 is a 3rd factor

multiply the 3 factors together

(x+1)(x^2+16)(x^-6)=0 is a polynomial with lowest degree, 5, that has the given roots or zeros

imaginary roots come in conjugate pairs, 4i and -4i

irrational roots also come in conjugate pairs, sqr6 and - sqr6