Find the Zeros for the Polynomial Function and Give the Multiplicity

question 211

Multiple Choice

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses
the x-axis or touches the x-axis and turns around, at each zero.
- $$f ( x ) = \frac { 1 } { 4 } x ^ { 2 } \left( x ^ { 2 } - 5 \right) ( x - 9 )$$

• A) 0 , multiplicity 2 , touches \(x\)-axis and turns around; 9 , multiplicity 1 , crosses \(x\)-axis;
• \(\sqrt { 5 }\), multiplicity 1 , crosses \(x\)-axis;
• \(- \sqrt { 5 }\), multiplicity 1 , crosses \(x\)-axis
• B) 0 , multiplicity 2 , crosses \(x\)-axis;
• 9, multiplicity 1 , touches \(x\)-axis and turns around;
• \(\sqrt { 5 }\), multiplicity 1 , touches \(x\)-axis and turns around;
• \(- \sqrt { 5 }\), multiplicity 1 , touches \(x\)-axis and turns around
• C) 0 , multiplicity 2 , touches \(x\)-axis and turns around;
• 9 , multiplicity 1 , crosses \(x\)-axis
• D) 0 , multiplicity 2 , touches \(x\)-axis and turns around;
• 9 , multiplicity 1 , crosses \(x\)-axis
• 5 , multiplicity 2 , touches \(x\)-axis and turns around

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Definitions:

Developmental Psychopathology

The study of the evolution of psychological disorders, with an emphasis on the interplay between biological, psychological, and social factors over the life span.

Comorbidity

The occurrence of two or more disorders or diseases in the same person, either simultaneously or sequentially.

Multifinality

The principle that similar early experiences or conditions can lead to different outcomes in psychological development or behavior.

Specific Learning Disorder

A marked deficit in a particular area of learning that is not caused by an apparent physical disability, by an intellectual disability, or by an unusually stressful home environment.