How do you write a polynomial in standard form given zeros #-2# and #1 + 2i#?

Question

4258 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-09-01T02:33:19

The desired polynomial is
#x^2+(1-2i)x-2-4i#

If #a#, #b# and #c# are the zeros of a polynomial, then the polynomial is

#(x-a)(x-b)(x-c)#.

Hence, the polynomial with zeros as #-2# and #1+2i# will be

#(x-(-2))(x-(1+2i))# or

#(x+2)(x-1-2i)# or

#x(x-1-2i)+2(x-1-2i)# or

#x^2-x-2ix+2x-2-4i# or

#x^2+x-2ix-2-4i# or

#x^2+(1-2i)x-2-4i#