# How do you write a polynomial function of least degree that has real coefficients, the following given zeros 3-i,5i and a leading coefficient of 1?

Any polynomial with real coefficients and imaginary or complex zeros, must have zeros that are conjugate pairs, therefore, the polynomial must have the following factors:

Multiplying the last two factors is easy; it is the sum of two squares:

Multiplying the first two factors is a bit more difficult:

Combine like terms:

Multiply the remaining factors:

Combine like terms:

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To write a polynomial function with real coefficients and the given zeros, you can use the complex conjugate theorem. Since the zeros given are 3-i, 5i, and 3+i (since complex zeros always come in conjugate pairs), the factors of the polynomial are (x - 3 + i), (x - 3 - i), and (x - 5i). Multiplying these factors together gives the polynomial function.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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