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## Find the polynomial of minimum degree, with real coefficients, zeros at x=4+4i and x=2, and y-intercept at 64

Question

Find the polynomial of minimum degree, with real coefficients, zeros at x=4+4i and x=2, and y-intercept at 64

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Mathematics
3 years
2021-08-21T20:54:05+00:00
2021-08-21T20:54:05+00:00 1 Answers
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## Answers ( )

Answer:Step-by-step explanation:We want to find the minimum-degree polynomial with real coefficients and zeros at:

As well as a

y-intercept of 64.By the Complex Root Theorem, if

a+bi is a root, thena–bi is also a root.So, a third root will be 4 – 4i.

The factored form of a polynomial is given by:

Where

ais the leading coefficient andpandqare the zeros. More factors can be added if necessary.Substitute:

Since we want the minimum degree, we won’t need to add any exponents.

Expand the second and third factors:

Hence:

Lastly, we need to determine

a. Since they-intercept isy= 64, this means that whenx= 0,y= 64. Thus:Solve for

a:Our factored polynomial is:

Finally, expand: