## The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45. The actual roots odered from least to greatest are and .

Question

The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45. The actual roots odered from least to greatest are and .

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The actual roots ordered from least to greatest are -45, -15, -9, -5, -3, -1, 1, 3, 5, 9, 15, 45

Step-by-step explanation:

To order negative and positive numbers you have to remember that the negative value with the greatest absolute value is the least value of the list, and all negatives values are less than the positive ones. For the positive values, the greatest absolute value is the greatest value of the list.

Complete the steps to find all zeroes of the function f(x) = x4 − 4×3 − 4×2 + 36x − 45.

This function has  4  roots.

The possible rational roots are ±1, ±3, ±5, ±9, ±15, and ±45.

The actual roots ordered from least to greatest are  -9  ⇒ -3 and
3

Partially factored form:

f(x) = (x − 3)(x + 3)(x2− 4x + 5)

Use the quadratic formula to identify the zeroes of x2 − 4x + 5.

x = 2 + i and 2 – i

Fully factored form:

f(x) = (x − 3)(x + 3)[x − (2 − i)][x − (2 + i)]

The function has 2  real roots and 2  imaginary roots.