What is the polynomial, in factored form, for the function

chezmarylou1i

chezmarylou1i

Answered question

2021-12-13

What is the polynomial, in factored form, for the function with the leading coefficient 6, and zeros 2, -3 multiplicity 2, 5i, and -5i ?

Answer & Explanation

alexandrebaud43

alexandrebaud43

Beginner2021-12-14Added 36 answers

Step 1
We find a polynomial function of leading coefficient 6 and zeros 2,-3 multiplicity 2 5i and -5i
Step 2
Let F(x) be the polynomial function.
Since 2 and -3 be the zeros of f(x) of multiplicity of 2.
So, (x2)2 and (x+3)2 is a factor of F(x)
Since 5i and -5i be the zeros of f(x)
So, (x-5i) and (x+5i) be the factor of f(x)
Here leading coefficient = 6
So F(x)=6(x2)2(x+3)2(x+5i)(x5i)
=6(x2)2(x+3)2(x225i2)
=6(x2)2(x+3)2(x2+25)

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