Both problems please :) Write the polynomial as the product of linear factors g(

Question

Both problems please :) Write the polynomial as the product of linear factors g(x)-x4-6x3 + 11x2-24x + 36 gix) List all the zeros of the function. (Enter your answers as a comma-separated list.) Need Help? Tak t Tor My Notes Ask Your Te Find all the zeros of the function When there zeros that are obviously not zeros of the function (Enter your answers as a comma separated list.) e is an estended ist of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational Nood Help?

Explanation / Answer

1) Given function, g(x) = x4 - 6x3 + 13x2 - 24x + 36

i.e., g(x) = (x - 3)(x3 - 3x2 + 4x - 12)

i.e., g(x) = (x - 3)(x - 3)(x2 + 4)

i.e., g(x) = (x - 3)2(x2 + 4)

Now, we are going to find all the zeros of the given function.

i.e., g(x) = 0

i.e., (x - 3)2(x2 + 4) = 0

i.e., x = 3,3,2i,-2i [where i2 = -1]

2) Given function is f(x) = 3x4 + 13x3 + 7x2 + 13x + 4

We are going to find all zeroes (approaximately zeros) of the given function.

Therefore, x =  -0.33333333333352666,   9.725553695716371e-14 +i* 0.9999999999999798,

9.725553695716371e-14 -i* 0.9999999999999798, -4.000000000000001.

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