Question

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

Answer 1

`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"`