Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$

question 45

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

• A) \(x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1\)
• B) \(x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1\)
• C) \(x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1\)
• D) \(x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2\)
• E) \(x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1\)

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Definitions:

BIOS

Basic Input/Output System, firmware code embedded on a computer's motherboard that initializes hardware components during the booting process and provides runtime services for operating systems and programs.

POST

Power-On Self Test, a series of diagnostic tests that a computer's firmware runs to check the hardware components and ensure no errors exist before the operating system loads.

Boot Process

The sequence of operations that a computer system performs from the moment it is turned on until it is ready for use, involving hardware and software initialization to load the operating system.

BIOS

Basic Input/Output System, firmware that initializes and tests hardware during the startup process of a computer.