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P5.3: Roots/Zeros & Multiplicity

Last updated almost 4 years ago
15 questions
Note from the author:
For a review of how zeroes relate to the graph, watch this video.
For more review and a discussion of multiplicity, watch this video.

You will find Desmos helpful for this homework.
For a review of how zeroes relate to the graph, watch this video.
For more review and a discussion of multiplicity, watch this video.

You will find Desmos helpful for this homework.
1

Find the zeros of the function.

f(x) = x2(x-1)4(x+5)

Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

1

Which root from f(x) = x2(x-1)4(x+5) has a multiplicity of 2?

Enter your answer as a number (the x-value of the root), no spaces.

1

Find the zeros of the function.

f(x) = x3 - 12x2 + 35x

Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

1

Which best describes the graph of the function in #3?

1

Find the zeros of the function.

f(x) = -8x3 - 20x2

Use x={#, #} format, with exactly one space after the comma. List the roots in increasing order.

1

For #5, at which root does the graph bounce?

Enter your answer as a number, no spaces.

1

For #5, at which root does the graph pass through the x-axis?

Enter your answer as a number, no spaces.

1

A polynomial has zeros at -1, 2, and 7, all with multiplicity 1. In addition, its leading coefficient is 1. Write the function in standard form.

Use c1x3 + c2x2 + c3x + c4 format, no spaces, with cn being your coefficients.

1

A polynomial has zero at 0 with multiplicity 1, a zero at 1 with multiplicty 2, and a zero at 5 with multiplicity 1. In addition, its leading coefficient is 1. Write the function in standard form.

Use c1x4 + c2x3 + c3x2 + c4x format, no spaces, with cn being your coefficients.


STUDY this and #8. There will be one like this on the quiz.

1

Find the zeros of the function.

f(x) = x3 - 10x2 + 27x - 18

Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

1

Find the zeros of the function.

f(x) = -x4 - 7x3 - 12x2

Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

1

Review

Categorize the functions according to their end behaviors.

This will turn green when all answers are in the right spot

  • 5x^{5} + 64x
  • x^{2} + 3x - 5
  • 4x
  • an odd degree polynomial with a negative leading coefficient
  • a binomial with a negative leading coefficient
  • an odd degree polynomial with a positive leading coefficient
  • 1 - x
  • 2 - x^{2}
  • 6 - x^{3}
  • x\rightarrow\infty, f(x)\rightarrow\infty;
    x\rightarrow -\infty, f(x)\rightarrow \infty
  • x\rightarrow\infty, f(x)\rightarrow\infty;
    x\rightarrow -\infty, f(x)\rightarrow -\infty
  • x\rightarrow\infty, f(x)\rightarrow -\infty;
    x\rightarrow -\infty, f(x)\rightarrow \infty
  • x\rightarrow\infty, f(x)\rightarrow -\infty;
    x\rightarrow -\infty, f(x)\rightarrow -\infty
  • Not enough info
1
Consider the function

f(x) = x^{3} -3x + 1

f(x) is increasing on __________ and decreasing on __________.
f(x) has a relative max at __________ and a relative min at __________.
f(x) has a range of __________.
1

REVIEW

Write the polynomial in standard form, no spaces.

2x(x+1)^{2} - (5x^{2} - x)

1

REVIEW

Write the quotient in standard form, no spaces.

\frac{3x^{4} - 72x + 9x^{2}}{3x}