P5.3: Roots/Zeros & Multiplicity

Last updated over 4 years ago

15 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Akwankyerɛ

P5.3: Roots/Zeros & Multiplicity

Last updated over 4 years ago

15 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

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.

Akwankyerɛ

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?

The graph bounces at one zero, and passes across the x-axis at two zeroes.

The graph bounces at two zeroes, and passes across the x-axis at the other.

The graph passes across the x-axis at all of its zeroes.

The graph bounces at all of its zeroes.

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 c_n 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 c_n 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

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

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

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 c_n 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 c_n 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 c_n 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 c_n 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}