Characteristics of the Zeros of Polynomial Functions

Characteristics of the Zeros of Polynomial Functions

By rene verula

Multiple Choice

find the zeros of the given function using the rational root theorem and synthetic division. f(x)= 8x³ - 12x² - 2x + 3

1. How many positive and negative zeros does the function have?

• all zeros are positive

• 2 negative and 1 positive

• 2 positive and 1 negative

• all zeros are negative

Multiple Choice

2. Between which consecutive integers is each zero located?

• -2 and 1; 1 and 2; 2 and 3

• -1 and 0; 0 and 1; 1 and 2

• -3 and -2; -1 and 0 2 and 3

Multiple Choice

3. What is the least integer greater than the highest zero of the function? What is the greatest integer less than the lower zero of the function?

• 2 ; -1

• 4 ; -2

• 5 ; -1

Multiple Choice

Determine the number of positive and negative real zeros of the function.

f(x)= -3x³  + 4x² - 2x + 1

• Number of positive zeros: 0 ; Number of negative zero: 3

• Number of positive zeros: 4 or 2 ; Number of negative zero: 1

• Number of positive zeros: 3 or 1 ; Number of negative zero: 0o

• Number of positive zeros: 3 or 1 ; Number of negative zero: 2

Multiple Choice

Determine between which consecutive integers the real zeros of the function f(x)= 2x⁴ + 4x³ -9x + 1 are found.

• between 0 and 1 ; between 1 and 2

• between -1 and 0 ; between 2 and 3

• between 0 and 1 ; between 1 and 2

Multiple Choice

Determine the least lower bound and the greatest lower bound of f(x) = 5x³ +2x² -3x -1.

• 1 and -1 respectively

• 1/5 and -1/5 respectively

• 5 and -5 respectively