Find a degree 3 polynomial with real coefficients having zeros

John Stewart

John Stewart

Answered question

2022-01-17

Find a degree 3 polynomial that has a lead coefficient of 1 and real coefficients with zeros 4 and 4i. Write PP in expanded form. Write the entire equation down, including P(x)=.

Answer & Explanation

Bob Huerta

Bob Huerta

Beginner2022-01-18Added 41 answers

Step 1 
Explanation:
Find 3 degree polynomial: 
Zeros include 4, 4, and the result of 4i=-4i, which is also a zero.
Step 2 
P(x)=(x-4)(x-4i)(x+4i) 
=(x4)(x24i2)   i2=1 
=(x4)(x2+4) 
=x(x2+4)4(x2+4) 
=x3+4x4x216 
P(x)=x34x2+4x16

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