SOLUTION: f(x) = x4 − 12x3 + 37x2 − 12x + 36 (a) Find all zeros of the function. (Enter your answers as a comma-separated list.) x = I found this to be i,-i,6 (b) Write the

SOLUTION: f(x) = x4 − 12x3 + 37x2 − 12x + 36 (a) Find all zeros of the function. (Enter your answers as a comma-separated list.) x = I found this to be i,-i,6 (b) Write the

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Question 1183370: f(x) = x4 − 12x3 + 37x2 − 12x + 36
(a) Find all zeros of the function. (Enter your answers as a comma-separated list.)
x = I found this to be i,-i,6

(b) Write the polynomial as a product of linear factors.
f(x) =

(c) Use your factorization to determine the x-intercepts of the graph of the function. Use a graphing utility to verify that the real zeros are the only x-intercepts. (Enter your answers as a comma-separated list. If no x-intercepts exist, enter DNE.)
x =

Answer by Solver92311(821) (Show Source): You can put this solution on YOUR website!

Your answer to part a is incorrect. Since you started with a 4th-degree polynomial, the fundamental theorem of algebra demands that you have 4 zeros counting multiplicities. You only list 3. Hint: One of your listed zeros has a multiplicity of 2.

If

is a zero of a polynomial, then

is a factor of the polynomial. Since you have four zeros, you need to have four factors.

Any real number zeros are

-intercepts. Hint: when you have an even-numbered multiplicity, the graph is tangent to the

-axis.

John

My calculator said it, I believe it, that settles it

From
I > Ø

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