How do you write the polynomial with zeros; 5, 4i, -4i?

1 Answer
Feb 25, 2018

Answer:

#f(x)=x^3-5x^2+16x-80#

Explanation:

#"given the zeros of a polynomial, say"#

#x=a,x=b" and "x=c#

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

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

#f(x)=a(x-a)(x-b)(x-c)larrcolor(blue)"a is a multiplier"#

#"here "x=5,x=4i" and "x=-4i" are the zeros"#

#rArr(x-5),(x-4i),(x+4i)" are the factors"#

#f(x)=a(x-5)(x-4i)(x+4i)#

#"let "a=1#

#rArrf(x)=(x-5)(x^2+16)#

#color(white)(rArrf(x))=x^3-5x^2+16x-80larr"possible polynomial"#