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find the polynomial function

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find the polynomial function f (x) with real coefficients having the given degree and zeros answer will vary depending on the choice of the leading coefficient.

Degree 4 ; zeros 3 + 2i , 4,multiplicity 2

 

asked Jan 21, 2015 in PRECALCULUS by anonymous
edited Jan 21, 2015 by bradely

1 Answer

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Step 1 :

The degree of image is image, the zeros are image, image and the multiplicity is image.

Since the degree of the polynomial is image, the zeros of image are image.

From the conjugate pair theorem, complex zeros occur in conjugate pairs.

Conjugate of image is image.

Since the multiplicity is image, the remaining zero is image.

The four zeros are image.

Step 2 :

If image are the zeros of the polynomial image, then the polynomial function can be written as image, where image is the leading coefficient of the polynomial.

Consider the leading coefficientimage as image.

image

image

Hence, the polynomial function is image and image.

Solution :

The polynomial function is image and image.

answered Jan 21, 2015 by lilly Expert
edited Jan 21, 2015 by lilly

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