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

Ryann Hart

Ryann Hart

Answered question

2023-03-23

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

Answer & Explanation

Jocelynn Vega

Jocelynn Vega

Beginner2023-03-24Added 5 answers

Given solution:
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 ) a is a multiplier
here x = 5 , x = 4 i and x = - 4 i are the zeros
( x - 5 ) , ( x - 4 i ) , ( x + 4 i ) are the factors
f ( x ) = a ( x - 5 ) ( x - 4 i ) ( x + 4 i )
let a = 1
f ( x ) = ( x - 5 ) ( x 2 + 16 )
f ( x ) = x 3 - 5 x 2 + 16 x - 80 possible polynomial

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