How do find all zeros of the function?

#g(x)=x^(4)-3x^(3)-x^(2)-12x-20#

#x=2i#

1 Answer
Jan 2, 2018

Answer:

#x=+-2i,x=(3+-sqrt(29))/2#

Explanation:

We have been given that #x=2i# is a zero. Since complex solutions to polynomials with real coefficients always come in conjugate pairs (the imaginary parts need to cancel), we know that #x=-2i# is also a solution.

This means that #(x-2i)(x+2i)=x^2+4# is a factor of the polynomial, and we can find out the remainder using polynomial long division:
#(x^2+4)(x^2-3x-5)#

We can solve for when the quadratic factor equals zero using the quadratic formula:
#x=(3+-sqrt(29))/2#