2.4: Zeros of Polynomial Functions

Multiple Choice

List all possible rational zeros of f(x). Then determine which are zeros.?

• $$x=1\ ,\ x=\ \sqrt[]{7}$$  

• $$x=1$$  

• $$x=1\ ,\ x=\ \sqrt[]{7},\ x=-\ \sqrt[]{7}$$  

Multiple Choice

List all possible rational zeros of f(x). Then determine which are zeros.?

• $$x=2\ ,\ x=∓3𝑖$$  

• $$x=2$$  

• $$x=∓3𝑖$$  

Multiple Choice

• $$𝟔\ and\ \frac{-1}{2}.$$  

• $$\ \ \frac{-1}{2}$$  

• $$6$$  

Multiple Choice

• h(x) has 3 variation in sign, h(x) has 3 positive real zeros.h(-x) has 1 variations in sign, h(x) has 1 negative real zero.

• h(x) has 2 variation in sign, h(x) has 2 positive real zeros.h(-x) has 1 variations in sign, h(x) has 1 negative real zero.

• h(x) has 4 variation in sign, h(x) has 4 positive real zeros.h(-x) has 1 variations in sign, h(x) has 1 negative real zero.

• h(x) has 5 variation in sign, h(x) has 5 positive real zeros.h(-x) has 1 variations in sign, h(x) has 1 negative real zero.

Multiple Choice

• $$𝒇(𝒙)=𝒙^𝟒−𝟒𝒙^𝟑−𝟐𝟑𝒙^𝟐+𝟓𝟒𝒙+𝟕𝟐$$  

• $$𝒉(𝒙)=𝟐𝒙^𝟒−𝟏𝟏𝒙^𝟑+𝟐𝒙^𝟐−𝟒𝟒𝒙−𝟐𝟒$$  

• $$𝒉(𝒙)=−𝟏𝟏𝒙^𝟒+𝟐𝟎𝒙^𝟑+𝟑𝒙^𝟐−𝒙+𝟏𝟖$$  

Multiple Choice

•    $$𝐟(𝒙)=𝒙^𝟑+𝟓𝒙^𝟐−𝟒𝒙−𝟐$$  

•   $$𝒇(𝒙)=𝒙^𝟒−𝟔𝒙^𝟑−𝟏𝟒𝒙^𝟐−𝟏𝟓𝟒𝒙−𝟐𝟓𝟓$$  

•      $$𝒈(𝒙)=〖𝟐𝒙〗^𝟑−𝟒𝒙^𝟐+𝟏𝟖𝒙−𝟑𝟔$$  

Multiple Choice

• x=-4 , x=3 , x=1/2  , x=3-i as Zeros   

  (x+4)(x-3)(x-1/2)(x-(3-i)) as Factors 

•  x=-4 , x=3 , x=1/2  , x=3-i , x=3+i as Zeros   

  (x+4)(x-3)(x-1/2)(x-(3-i))(x-(3+i)) as Factors 

Open Ended

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