Rational root theorems are used to determine the potential roots of a polynomial function
The actual roots are 3 and -4The potential roots are [tex]\pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]The function is given as:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
Expand
[tex]f(x) = 2x^2 + 8x - 6x - 24[/tex]
Expand
[tex]f(x) = 2x(x + 4) - 6(x + 4)[/tex]
Factor out x + 4
[tex]f(x) = (2x -6)(x + 4)[/tex]
Set to 0
[tex](2x -6)(x + 4) = 0[/tex]
Split
[tex](2x -6) = 0\ or\ (x + 4) = 0[/tex]
Make x the subject in both cases
[tex]2x = 6\ or\ x= -4[/tex]
Solve for x
[tex]x = 3\ or\ x= -4[/tex]
So, the actual roots are 3 and -4
Recall that, the function is:
[tex]f(x) = 2x^2 + 2x - 24[/tex]
For a function,
[tex]f(x) = px^n + ax^{n-1} +.......+q[/tex]
According to rational root theorem, the roots of f(x) are:
[tex]Roots = \pm \frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
The roots of 24 are:
[tex]24 = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
The roots of 2 are:
[tex]2 = \pm1, \pm2[/tex]
So, the possible roots are:
[tex]Roots = \frac{\pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24}{\pm 1, \pm 2}[/tex]
This gives:
[tex]Roots = \pm1, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24,\pm0.5, \pm1, \pm 1.5, \pm 2, \pm 3, \pm 4, \pm6\pm 12[/tex]
Remove repetitions
[tex]Roots = \pm0.5, \pm1, \pm 1.5, \pm2, \pm 3, \pm 4, \pm 6, \pm 8, \pm12,\pm 24[/tex]
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3 and -4 dudes and dudettes
edg2022
The shortest side of a right triangle measures 16 m. The lengths of the other two sides are consecutive . Find the lengths of the other two sides.
Answer:
this is hard
Step-by-step explanation:
I bad at math :/ plz help
Answer:
i think its b
Answer:
B. (x³-10)(x⁶+10x³+100)
Step-by-step explanation:
x⁹-1000
(x³)³-10³
so now always remember
x³-y³=(x-y)(x²+xy+y²)
so for this question x= x³ and y=10
we now have
(x³-10)((x³)²+10x³+10²)
(x³-10)(x⁶+10x³+100)
Solve for x. 7x+8>4x+4
Hence, the inequality is x > -4/3.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Answer:
x > - [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
7x + 8 > 4x + 4 ( subtract 4x from both sides )
3x + 8 > 4 ( subtract 8 from both sides )
3x > - 4 ( divide both sides by 3 )
x > - [tex]\frac{4}{3}[/tex]
P(x)=3x 4 −2x 3 +2x 2 −1P, left parenthesis, x, right parenthesis, equals, 3, x, start superscript, 4, end superscript, minus, 2, x, cubed, plus, 2, x, squared, minus, 1 What is the remainder when P(x)P(x)P, left parenthesis, x, right parenthesis is divided by (x+1)(x+1)left parenthesis, x, plus, 1, right parenthesis?
The remainder when the polynomial is divided by x + 1 is 2
Given the function P(x)=3x^4 −2x^3 +2x^2 −1, to get the rmainder if the polynomial is divided by x + 1, we will substitute x = - 1 into the function to have:
P(-1) = 3(-1)^4 −2(-1)^3 +2(-1)^2 −1
P(-1) = 3(1) - 2 + 2(1) - 1
P(-1) = 1 + 1
P(-1) = 2
Hence the remainder when the polynomial is divided by x + 1 is 2
Learn more on polynomials here: https://brainly.com/question/4142886
Answer:
6
Step-by-step explanation:
:)
which expression is equivalent to the expression (2x+4)(x-6) pls i need it
Answer:
[tex]B.~2x^2-8x-24[/tex]
Step-by-step explanation:
FOIL the terms and then add like terms.
[tex]2x\cdot x=2x^2\\2x\cdot -6=-12x\\4\cdot x=4x\\4\cdot -6=-24\\\\2x^2-12x+4x-24\\2x^2-8x-24[/tex]
want to check my answer
Answer:
Yes. The answer is good 3x+1
Please help me out
Fill in the blanks for this graph
1. This graph crosses the y-axis at______
2. The graph increases in the interval_____
3. The graph decreases in the interval____
Answer:
1 -5
don't know the answer of q2 and q3
Express 0.16 bar as a rational number
that was sooo good !
Jose has scored 854 points on his math tests so far this semester. To get an A for the semester, he must score at least 876 points.
Answer:
It is 22
Step-by-step explanation:
х2 + 2x, 3х + 5, x2 + 1, 6x - 4
Answess
Step-by-step explanation:
wahts the gcf and lcm of 18 and 30
Ned had 76 boxes. together the boxes weighed 723 kilograms. About how much did each box weigh
Answer: ~9.51 kilograms each.
Step-by-step explanation: 723/76=9.5131
Help me with my math work please! Whoever helps gets 50 points! Thnx!
Answer:
6) y=-2
7) w=15
8) x=1
Which polynomial is prime? x4 3x2 â€"" x2 â€"" 3 x4 â€"" 3x2 â€"" x2 3 3x2 x â€"" 6x â€"" 2 3x2 x â€"" 6x 3.
The polynomial [tex]3x^2+x-6x+3[/tex] is a prime because it is not factorized further and this can be determined by using the factorization method.
Check all the options in order to determine the given polynomial is prime or not.
A) [tex]x^4+3x^2-x^2-3[/tex]
Now, try to factorize the above polynomial.
[tex]x^4+3x^2-x^2-3=(x+1)(x-1)(x^2+3)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
B) [tex]x^4-3x^2-x^2+3[/tex]
Now, try to factorize the above polynomial.
[tex]x^4-3x^2-x^2+3=(x+1)(x-1)(x^2-3)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
C) [tex]3x^2+x-6x-2[/tex]
Now, try to factorize the above polynomial.
[tex]3x^2+x-6x-2=(3x+1)(x-2)[/tex]
The given polynomial is factorized further therefore, this polynomial is not a prime.
D) [tex]3x^2+x-6x+3[/tex]
The given polynomial is not factorized further therefore, this polynomial is is a prime.
For more information, refer to the link given below:
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The number of feet in an unknown
number of yards. Let b = the variable.
Algebraic expression:
There are 3feet in one yard.
Let B = number of feet
Let Y = number of yards
B = 3Y
solve the following quadratic equation
27x^2 = 3
27x^2 - 3 = 0
3(9x^2 - 1 ) = 0
9x^2 - 1 = 0
( I think this is it- )
What is the next term of the geometric sequence?
108, 36, 12,
Pls lmk
Answer:
4
Step-by-step explanation:
Answer: 4
Step-by-step explanation: 108/3 is 36, 36/3 is 12, and 12/3 is 4. :)
What is the coefficient in this expression? (34mn)
34
3
n
4
The coefficient in this expression is 34.
The first option is the correct answer.
What are variables and coefficients?The variable can have any value. That is, you can change the value of the variable. The value of the coefficient does not change, but changes in the value of the variable can change the value of the term containing the variable and the coefficient.
In formulas, coefficients are constants that are multiplied by variables. Consider the following equation: 3 x 2 + 5x-3 = 0. ax3 + x 2 = z. The values 3 and 5 in the first equation are the coefficients of the variable x.
Learn more about coefficient of expression here https://brainly.com/question/525935
#SPJ2
what is the product of 9,028 x 100,000
Answer:
902,800,000
Step-by-step explanation:add the 5 zeros from 100,000 to 9,028
line has equation 3x + y = 15
Find the gradient of the line.
Answer:
-3
Step-by-step explanation:
We can add -3x to put the equation into slope-intercept form.
y = -3x +15
The gradient of the line (slope) is the coefficient of x: -3.
The gradient is -3.
help me with this question plzzzzzzz
Answer:
The base is 9.4 milliliters
Step-by-step explanation:
First, you would notice that they give you the perimeter of it. Meaning 51.4 was a sum of adding the height and base length twice. So you would take 51.4 and subtract 16*2 from it. Which would be 19.4. Next, since 19.4 would be both bases added, and they are both the same, you would do 19.4/2=9.4
The base is 9.4 milliliters.
Answer:
9.7
Step-by-step explanation:
P=2B+2H=51.4
B+H=25.7
H=16
B=25.7-16
B=9.7
Translate each of the following algebraic expressions into word phrase.
7x-7
Can you please help me with this question
Answer:
C
Step-by-step explanation:
The first step in solving a problem is to understand what you are given. Here, all of the tables have the same set of equally-spaced x-values. That means a linear relationship can be identified by looking for constant differences in the f(x) values.
Only the f(x) values in Table C have constant differences (all are 2).
Table C represents a linear function. f(x) = 2x -1
A rectangle has a perimeter of 44 inches and an area of 72 square inches. What are the lengths of the sides of the rectangle?
A) 2 inches and 36 inches
B) 4 inches and 18 inches
C) 8 inches and 9 inches
D) 11 inches and 11 inches
IT IS NOT D, I TRIED IT AND IT DOESNT WORK!
or, l + b = 22
or, b = 22 - l ...(i)
We know, area of a rectangle = lbTherefore,lb = 72Putting (i) in b, we getl(22 - l) = 72or, 22l - l^2 -72 = 0
or, l^2 - 22l + 72 = 0
or, l^2 - 4l - 18l + 72 = 0
or, l(l - 4) - 18(l - 4) = 0
or, (l - 4)(l - 18) = 0
or, l = 4 or l = 18
Therefore, if the length is 4 inches, then the breadth is (22-4) inches, i.e., 18 inches.And if the length is 18 inches, then the breadth is (22-18) inches, i.e., 4 inches.Answer:
B) 4 inches and 18 inches.
Hope you could get an idea from here.
Doubt clarification - use comment section.
3.52 in expanded form
Step-by-step explanation:
3.52 =
3
+ 0.5
+ 0.02
hopes this helps you
ASAPPPP HELPPPP PLEASEEEE
Answer:
27.6
Step-by-step explanation:
sin29=x/57
0.48480962=x/57
x≈27.6
Algún jefazo:)))))))))))
Answer:
Step-by-step explanation:
PLSSSS HELP I WILL GIVE BRAINLIEST
Which statements are true about the ordered pair (7, 19) and the system of equations?
{2x−y=−5x+3y=22
Select each correct answer.
The ordered pair (7, 19) is a solution to the first equation because it makes the first equation true.
The ordered pair (7, 19) is a solution to the second equation because it makes the second equation true.
The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (7, 19) is a solution to the system because it makes both equations true.
Answer: The ordered pair (7, 19) is not a solution to the system because it makes at least one of the equations false.
Step-by-step explanation:
In the ordered pair (7,19), 7 is the x and 19 is the y. Plug those in and multiply.
2(7)-19=-5
-5=-5
7+3(19)=22
64 doesn't =22
SO, one part of the equation is wrong making the ordered pair wrong.
The perpendicular bisector of a line segment is called
Answer:
Circumcenter
Step-by-step explanation:
