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
Algebra ->
Functions
-> 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
Log On
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 =
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
