The following equation is given.x3-3x-4x+12=0Xa. List all rational roots that are possible according to the Rational Zero Theorem.(Use a comma to separate answers as needed.)one actual rootb. Use synthetic division to test several possible rational roots in order to identifyOne rational root of the given equation is(Simplify your answer)C. Use the root from part (b.) and solve the equationThe solution set of x-3x-4x + 12 0 is(Simplify your answer. Typeanswers as needed.)or fractions for any numbers in the expresXan exact answer, using radicals as needed. Use integersEnter your answer in each of the answer boxese to searchhpHE WLET T PACKA R Df4f6f7fBf9ha+$4&756826

Question
Asked Aug 8, 2019
The following equation is given.
x3-3x-4x+12=0
X
a. List all rational roots that are possible according to the Rational Zero Theorem.
(Use a comma to separate answers as needed.)
one actual root
b. Use synthetic division to test several possible rational roots in order to identify
One rational root of the given equation is
(Simplify your answer)
C. Use the root from part (b.) and solve the equation
The solution set of x-3x-4x + 12 0 is
(Simplify your answer. Type
answers as needed.)
or fractions for any numbers in the expres
X
an exact answer, using radicals as needed. Use integers
Enter your answer in each of the answer boxes
e to search
hp
HE WLET T PACKA R D
f4
f6
f7
fB
f9
ha
+
$
4
&
7
5
6
8
26
help_outline

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The following equation is given. x3-3x-4x+12=0 X a. List all rational roots that are possible according to the Rational Zero Theorem. (Use a comma to separate answers as needed.) one actual root b. Use synthetic division to test several possible rational roots in order to identify One rational root of the given equation is (Simplify your answer) C. Use the root from part (b.) and solve the equation The solution set of x-3x-4x + 12 0 is (Simplify your answer. Type answers as needed.) or fractions for any numbers in the expres X an exact answer, using radicals as needed. Use integers Enter your answer in each of the answer boxes e to search hp HE WLET T PACKA R D f4 f6 f7 fB f9 ha + $ 4 & 7 5 6 8 26

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check_circleExpert Solution
Step 1

a. Find the possible rational roots.

The possible rational roots of a polynomial equation x3-3x2-4x+12 = 0
The given polynomial equation is x -3x2-4x +12 0
Let f(x)x-3r2-4x +12
=
The constant term of the function is 12 and the leading coefficient is 1.
The factors of 1 is 1 and the factors of 12 are ±1, ±2, ±3, ± 4, ±6, 12
The factors of constant term, 12: t1, 2, 3, ±4, ±6, 12
The factors of leading coefficient, 1: 1
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The possible rational roots of a polynomial equation x3-3x2-4x+12 = 0 The given polynomial equation is x -3x2-4x +12 0 Let f(x)x-3r2-4x +12 = The constant term of the function is 12 and the leading coefficient is 1. The factors of 1 is 1 and the factors of 12 are ±1, ±2, ±3, ± 4, ±6, 12 The factors of constant term, 12: t1, 2, 3, ±4, ±6, 12 The factors of leading coefficient, 1: 1

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Step 2

The possible rational roots are computed as follows.

Factors of 12
Possible rational roots
Factors of 1
1, 2, 3, ± 4, 16, 12
1 +2 +3 +4 +6 12
-1, t2, t3, ±4, 6, 12
The possible rational roots of the polynomial function is twelve which are
1, 2, 3, 4, 6, 12.
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Factors of 12 Possible rational roots Factors of 1 1, 2, 3, ± 4, 16, 12 1 +2 +3 +4 +6 12 -1, t2, t3, ±4, 6, 12 The possible rational roots of the polynomial function is twelve which are 1, 2, 3, 4, 6, 12.

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Step 3

b. Identify the one actual r...

The actual root of the polynomial equation x3-3x- 4x+12 0 by using synthetic
division
Find a rational root among the possible rational roots, t1, 2, 13, t4, t 6, 12
Use the result, to find the roots of a polynomial function
Test with the number 1 from the possible rational roots
Write the coefficients of the polynomial equation x3 -3x2-4x +12
0 right of 1
1
-3
-4
12
1
2
-6
-6
1
-2
6
The remainder is not equal to zero, so 1 is not a rational root of the given equation
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The actual root of the polynomial equation x3-3x- 4x+12 0 by using synthetic division Find a rational root among the possible rational roots, t1, 2, 13, t4, t 6, 12 Use the result, to find the roots of a polynomial function Test with the number 1 from the possible rational roots Write the coefficients of the polynomial equation x3 -3x2-4x +12 0 right of 1 1 -3 -4 12 1 2 -6 -6 1 -2 6 The remainder is not equal to zero, so 1 is not a rational root of the given equation

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