Rational Root

Presentation

•

Mathematics

•

11th Grade

•

Hard

•

CCSS

HSA.APR.B.2, HSF-IF.C.7C, 8.EE.A.2

Standards-aligned

Jim Anthony

Used 6+ times

FREE Resource

6 Slides • 10 Questions

Multiple Choice

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

-3

-4

Multiple Choice

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ - 8x² - 23x + 30

-1

-10

Multiple Select

What is a rational number?

Decimals that end

Decimals that go on forever

Fractions

Negative Numbers

Irrational Numbers

If rational numbers can be written as fractions, the irrational numbers cannot.

Rational numbers

are ratios of two integers
if you can convert a number into a fraction it is a rational number
all positive and negative numbers
decimals that terminate or have repeating patterns

Examples of Rational numbers

Multiple Select

Select all that are rational numbers

0.24

-14.2

$2\ \frac{1}{5}$

$-\frac{5}{6}$

$0.\overline{3}$

Multiple Select

Which of these are perfect squares?

Square Roots: perfect squares

Irrational Numbers

Multiple Choice

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = x³ + 2x² - 6x + 8

±1, ±8

±1, ±2, ±4, ±8

±1, ±2, ±4

1, 2, 4, 8

Rational Root Theorem

If a polynomial has rational roots then the possible roots are:

Multiple Choice

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

±1,±2

±1,±3,±9

±1,±3±9,±1/2,±3/2,±9/2

±1,±2,±1/3,±2/3,±1/9,±2/9

Multiple Choice

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

±1, ±7, ±1/3, ±7/3

±1, 7

±1, ±3, ±7, ±7/3

±1, ±3, ±7, ±1/3, ±7/3

Multiple Choice

Solve by using Rational Root Theorem:
2x³ - 11x² + 12x + 9 = 0

-1, 1, 3

-1, 3/2, 3

-1/2, 3, 3

-1/2, 1, 3

Multiple Choice

Solve by using Rational Root Theorem:
x³ - 7x - 6 = 0

1, 2, 3

-1, -2, - 3

-1, -2, 3

1,-2,-3

Below are four possible zeros for this polynomial.

Figure out which one "works"

f(x) = x³ + 2x² - 11x - 12

-3

-4

Show answer

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MULTIPLE CHOICE

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