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now, suppose one of the roots of the polynomial function is complex. the roots of the function are 2+i, and 5. write the equation for this polynomial function. expand f(x)=x^3- __ x^2 + __ x- __

now suppose one of the roots of the polynomial function is complex the roots of the function are 2i and 5 write the equation for this polynomial function expand class=

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Lucyheartfilia0415

Answer:

f(x) = x³ - 9x² + 25x - 25

Step-by-step explanation:

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Using the concept of complex conjugate root theorem, if (2+i) is a root of polynomial P, (2-i) is also a root. Thus, making the polynomial to be

[tex]P = (x - 5)(x - (2 + i))(x - (2 - i))\\[/tex].

What is complex conjugate root theorem?

The complex conjugate root theorem states that if P is a polynomial in one variable with real coefficients, and a + bi is a root of P with a and b real numbers, then its complex conjugate a − bi is also a root of P.

So, given that (2 + i) is a root of the polynomial P, (2 - i)  should be a root as well.

The polynomial becomes:

[tex]P = (x - 5)(x - (2 + i))(x - (2 - i))\\[/tex]

Learn more about complex conjugate root theorem here

https://brainly.com/question/24904431

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