Write a polynomial f(x) that satisfies the given conditions. Degree 3

Lorraine Harvey

Lorraine Harvey

Answered question

2021-12-12

Write a polynomial f(x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.

Answer & Explanation

vicki331g8

vicki331g8

Beginner2021-12-13Added 37 answers

Step 1 
In this case, a polynomial function of 3 with the zeros 3i and 9/5 is written.
Step 2 
Let f(x) be the ploynomial function 
Given that 3i are the zeros of f(x), +3i are the zeros of f. (x)
[because complex conjugate each other] 
Since −3i be the zeros of f(x) then (x+3i) be the factor of f(x). 
Since +3i be the zeros of f(x) then (x−3i) be tge factor of f(x) 
Since 9/5 be the zeros of f(x) , then (x−9/5) be the factor of f(x). 
Step 3 
Therefore f(x)=(x+3i)(x−3i)(x−9/6) 
=(x2(3i)2)(x95) 
=x2(x95)+9(x95) 
=x39x25+9x815 
=x39x25+9x815 
Hence f(x)=x39x25+9x815

Nadine Salcido

Nadine Salcido

Beginner2021-12-14Added 34 answers

Zeros -3i and 95
Complex zero must have conjugate
x=±3i x=95
f(x)=(x3i)(x+3i)(x95)
=(x2(3i)2)(x95)
=(x2+9)(x95)
=x3+9x95x2815
=x395x2+9x815

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