Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.(x-6)(x+ 4)s0Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choiceO A. The solution set is(Simplity your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed Use integers or fractions for any numbers inthe expression.)O B. The solution set is the empty set.Which number line below shows the graph of the solution set?O B.-8O A.-8 -7 6765-2-1-3-7 -6-551-3 -2 -1-5-4OD-8O C.6 7 851-1-3-4-2-5-6-776-3 2 10 12 3-5-6-8 7Click to select your answeraryere to searchWhpT PACK AR Df3fsf610+12insprt scDIIdeletehome$&73568numlockbackspaceRTUPhoFKLenterCBpauseT shiftaltctrlOI

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Asked Aug 8, 2019
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Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation.
(x-6)(x+ 4)s0
Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice
O A. The solution set is
(Simplity your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed Use integers or fractions for any numbers in
the expression.)
O B. The solution set is the empty set.
Which number line below shows the graph of the solution set?
O B.
-8
O A.
-8 -7 6
7
6
5
-2-1
-3
-7 -6
-5
5
1
-3 -2 -1
-5-4
OD
-8
O C.
6 7 8
5
1
-1
-3
-4
-2
-5
-6
-7
7
6
-3 2 10 12 3
-5
-6
-8 7
Click to select your answer
ary
ere to search
W
hp
T PACK AR D
f3
fs
f6
10
+
12
ins
prt sc
DII
delete
home
$
&
7
3
5
6
8
num
lock
backspace
R
T
U
P
ho
F
K
L
enter
C
B
pause
T shift
alt
ctrl
O
I
help_outline

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Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. (x-6)(x+ 4)s0 Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The solution set is (Simplity your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed Use integers or fractions for any numbers in the expression.) O B. The solution set is the empty set. Which number line below shows the graph of the solution set? O B. -8 O A. -8 -7 6 7 6 5 -2-1 -3 -7 -6 -5 5 1 -3 -2 -1 -5-4 OD -8 O C. 6 7 8 5 1 -1 -3 -4 -2 -5 -6 -7 7 6 -3 2 10 12 3 -5 -6 -8 7 Click to select your answer ary ere to search W hp T PACK AR D f3 fs f6 10 + 12 ins prt sc DII delete home $ & 7 3 5 6 8 num lock backspace R T U P ho F K L enter C B pause T shift alt ctrl O I

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Expert Answer

Step 1

Calculation:

The given quadratic inequality is (x–6)(x+4)≤ 0.

Change the inequality sign by equal sign to form equivalent equation as (x–6)(x+4)=0.

Note that, if the product of two algebraic expressions is zero, then at least one of the factors is equal to zero.

use the note and solve the above equation as follows.

(x-6)(x+ 4) 0
x -6 0 or x+ 4 = 0
x 6 or x-4
The solution set is {-4,6}
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(x-6)(x+ 4) 0 x -6 0 or x+ 4 = 0 x 6 or x-4 The solution set is {-4,6}

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Step 2

The solutions divide the x axis into the intervals as  (–∞,–4), (–4,0), (0,6), and (6,∞).

Find the sign of the polynomial on each interval by selecting test value as follows.

Let the polynomial function be f(x)=(x–6)(x+4).

Obtain the sign of polynomial f(x) at the point x=–5 on the interval (–∞,–4).

 

f(-5) (-5-6)-5+4)
(11)
-11
0
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f(-5) (-5-6)-5+4) (11) -11 0

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Step 3

Obtain the sign of polynomial f(x) at the point x=&nda...

f(-1)(1-6)(-+4)
=(-7)(3)
=-21
< 0
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f(-1)(1-6)(-+4) =(-7)(3) =-21 < 0

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Equations and In-equations

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