Information is given about a complex polynomial whose coefficients are

Mary Hammonds

Mary Hammonds

Answered question

2021-12-10

Information is given about a complex polynomial whose coefficients are real numbers.Find the remaining zeros of f.Then find a polynomial function with real coefficients that has the zeros.
Degree 3; zeros: 4 +i, 6

Answer & Explanation

Bertha Jordan

Bertha Jordan

Beginner2021-12-11Added 37 answers

Step 1 
Given: 
Degree 3, zeros: 4+ i, 6 
Step 2 
Now, 
Degree 3, zeros: 4+ i, 6 
The complex root has always a pair with its conjugate. 
Hence, the third root is: 4-i 
therefore the polynomial will be: 
f(x)=(x-6)(x-(4+i))(x-(4i)) 
f(x)=(x6)(x2x(4i)x(4+i)+(4+i)(4i)) 
f(x)=(x6)(x28x+17) 
f(x)=x38x2+17x6x2+48x102 
f(x)=x314x26x2+65x102

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