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Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)

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Find a polynomial function with real coefficients that has the given zeros. (There are many correct answers.)

2/3, -1, 3 + √2 i

asked Jan 27, 2015 in TRIGONOMETRY by anonymous

1 Answer

0 votes

Step 1:

Complex zero of polynomial  function image and real zeros are image.

Using complex conjugate root theorem is a zero of the polynomial function.

Required polynomial is fourth degree polynomial.

Step 2:

Zeros are and .

By using Factor theorem,

When image then image is factor of polynomial.

image

 

image.

Solution:

The polynomial function image.

answered Jan 27, 2015 by david Expert
edited Jan 28, 2015 by bradely

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