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.

Instructions

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.

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.

Instructions

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.

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.

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.

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.

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

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.

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

Enter your answer as a number, no spaces.

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

Enter your answer as a number, no spaces.

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.

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.

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.

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.

Review

Categorize the functions according to their end behaviors.

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

an odd degree polynomial with a negative leading coefficient
5x^{5} + 64x
2 - x^{2}
4x
a binomial with a negative leading coefficient
1 - x
6 - x^{3}
x^{2} + 3x - 5
an odd degree polynomial with a positive leading coefficient

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

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 __________.

P5.3: Roots/Zeros & Multiplicity

P5.3: Roots/Zeros & Multiplicity

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.

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.

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.

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

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.

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

Enter your answer as a number, no spaces.

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

Enter your answer as a number, no spaces.

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.

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.

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.

Review

Categorize the functions according to their end behaviors.

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

REVIEW

Write the polynomial in standard form, no spaces.

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

REVIEW

Write the quotient in standard form, no spaces.

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

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.

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.

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.

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

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.

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

Enter your answer as a number, no spaces.

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

Enter your answer as a number, no spaces.

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.

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.

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.

Review

Categorize the functions according to their end behaviors.

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

REVIEW

Write the polynomial in standard form, no spaces.

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

REVIEW

Write the quotient in standard form, no spaces.

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

P5.3: Roots/Zeros & Multiplicity

P5.3: Roots/Zeros & Multiplicity

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.

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.

Find the zeros of the function.f(x) = x3 - 12x2 + 35xUse x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

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

Find the zeros of the function.f(x) = -8x3 - 20x2Use x={#, #} format, with exactly one space after the comma. List the roots in increasing order.

For #5, at which root does the graph bounce?Enter your answer as a number, no spaces.

For #5, at which root does the graph pass through the x-axis?Enter your answer as a number, no spaces.

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.

Find the zeros of the function.f(x) = x3 - 10x2 + 27x - 18Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

Find the zeros of the function.f(x) = -x4 - 7x3 - 12x2Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

ReviewCategorize the functions according to their end behaviors.This will turn green when all answers are in the right spot

REVIEWWrite the polynomial in standard form, no spaces.2x(x+1)^{2} - (5x^{2} - x)

REVIEWWrite the quotient in standard form, no spaces.\frac{3x^{4} - 72x + 9x^{2}}{3x}

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.

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.

Find the zeros of the function.f(x) = x3 - 12x2 + 35xUse x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

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

Find the zeros of the function.f(x) = -8x3 - 20x2Use x={#, #} format, with exactly one space after the comma. List the roots in increasing order.

For #5, at which root does the graph bounce?Enter your answer as a number, no spaces.

For #5, at which root does the graph pass through the x-axis?Enter your answer as a number, no spaces.

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.

Find the zeros of the function.f(x) = x3 - 10x2 + 27x - 18Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

Find the zeros of the function.f(x) = -x4 - 7x3 - 12x2Use x={#, #, #} format, with exactly one space after each comma. List the roots in increasing order.

ReviewCategorize the functions according to their end behaviors.This will turn green when all answers are in the right spot

REVIEWWrite the polynomial in standard form, no spaces.2x(x+1)^{2} - (5x^{2} - x)

REVIEWWrite the quotient in standard form, no spaces.\frac{3x^{4} - 72x + 9x^{2}}{3x}

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.

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.

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.

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.

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

Enter your answer as a number, no spaces.

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

Enter your answer as a number, no spaces.

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.

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.

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.

Review

Categorize the functions according to their end behaviors.

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

REVIEW

Write the polynomial in standard form, no spaces.

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

REVIEW

Write the quotient in standard form, no spaces.

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

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.

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.

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.

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.

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

Enter your answer as a number, no spaces.

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

Enter your answer as a number, no spaces.

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.

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.

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.

Review

Categorize the functions according to their end behaviors.

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

REVIEW

Write the polynomial in standard form, no spaces.

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

REVIEW

Write the quotient in standard form, no spaces.

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