Form a polynomial f(x) with real coefficients the given degree and zeros. Degree 4, Zeros:, 4-4i, -5 multiplicity 2

amanf

amanf

Answered question

2021-02-27

Form a polynomial f(x) with real coefficients the given degree and zeros. Degree 4, Zeros:, 4-4i, -5 multiplicity 2

Answer & Explanation

coffentw

coffentw

Skilled2021-02-28Added 103 answers

x-a is one of the polynomial's factors if an is its zero. Because complex conjugates are paired, 4+4i also equals a zero for f. (x). Both [x(44i)] and [x(4+4i)] are factors of f(x). 5 has a multiplicity of 2, hence it is equivalent to the factor
So, the polynomial is: f(x)=[x(44i)][x(4+4i)](x+5)2 
Expand: 
f(x)=[x2(4+4i)x(44i)x+(44i)(4+4i)](x2+10x+25) 
f(x)=[x24x+4ix4x+4ix+(1616i2)](x2+10x+25) 
f(x)=[x28x+(16+16)](x2+10x+25) 
f(x)=(x28x+32)(x2+10x+25) 
f(x)=x2(x28x+32)+10x(x28x+32)+25(x28x+32) 
f(x)=x48x3+32x2+10x380x2+320x+25x2200x+800 
f(x)=x4+2x323x2+120x+800

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