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

Lorraine Harvey 2021-12-12 Answered
Write a polynomial f(x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros −3i and 9/5.
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Expert Answer

vicki331g8
Answered 2021-12-13 Author has 37 answers
Step 1
Here we write a polynomial function of 3 with zeros −3i and 9/5.
Step 2
Let f(x) be the ploynomial function
Since −3i be the zeros of f(x) then +3i be also 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
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Nadine Salcido
Answered 2021-12-14 Author has 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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