How do you write a polynomial in standard form given the zeros x=2, -6, and 2+ 4i?

1 Answer
Sep 19, 2017

Answer:

#x^4-8x^2+128x-240#

Explanation:

#"given the zeros "x=a,x=b,x=c,x=d#

#"then the factors are "(x-a),(x-b),(x-c),(x-d)#

#"the polynomial is then the product of the factors"#

#p(x)=(x-a)(x-b)(x-c)(x-d)#

#"here one of the given zeros is complex " 2+4i#

#"complex zeros always occur in "color(blue)"conjugate pairs"#

#rArr2-4i" is also a zero of the polynomial"#

#"the four zeros are "x=2,x=-6,x=2+-4i#

#"4 zeros indicate a polynomial of degree 4"#

#rArrp(x)=(x-2)(x+6)(x-2-4i)(x-2+4i)#

#color(white)(rArrp(x))=(x^2+4x-12)(x^2-4x+20)#

#color(white)(rArrp(x))=x^4-8x^2+128x-240" possible polynomial"#