Answers
Given:
The zeros of the polynomial are [tex]-2,\pm 5,4[/tex].
Degree = 4
Leading coefficient = 1
To find:
The polynomial.
Solution:
If c is a zero of a polynomial, then (x-c) must be a factor of the polynomial.
Here, -2,4,-5, 5, are zeros of the required polynomial, so (x+2), (x-4), (x+5), (x-5) are factors of required polynomial.
[tex]p(x)=(x+2)(x-4)(x+5)(x-5)[/tex]
[tex]p(x)=(x^2-4x+2x-8)(x^2-5^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)=(x^2-2x-8)(x^2-25)[/tex]
Using distributive property, we get
[tex]p(x)=x^2(x^2-25)-2x(x^2-25)-8(x^2-25)[/tex]
[tex]p(x)=x^4-25x^2-2x^3+50x-8x^2+200[/tex]
On combining like terms, we get
[tex]p(x)=x^4-2x^3+(-25x^2-8x^2)+50x+200[/tex]
[tex]p(x)=x^4-2x^3-33x^2+50x+200[/tex]
Here, the leading coefficient is 1. So, it is the required polynomial.
Therefore, the correct option is E.
Related Questions
Please help me out!!!!!
Answers
Answer:
To find a degree 3 equation you must find and take the roots.You have the roots at x=0 Now plug those into the equation for example: (x-4) would result in x1=4Hope this helps!A recipe calls for 3 cups of sugar and 9 cups of water. How many should be used with 2 cups of sugar?
Answers
Answer:
6 cups of water
Step-by-step explanation:
A recipe calls for 3 cups of sugar and 9 cups of water. How many should be used with 2 cups of sugar?
The question above, is solved below:
3 cups of sugar = 9 cups of water
2 cups of sugar = x
Cross Multiply
3x = 9 × 2
x = 18/3
x = 6
Hence, 2 cups of sugar = 6 cups of water
A cone shape cup is made from a circular piece of paper of radius 7 by cutting out a sector and joining the edge AC and BC. Find the maximum (volume) of such a cup
Answers
Answer:
The answer is "138.10"
Step-by-step explanation:
Let r also be cone base radius and h = the cone height.
The radius for the original circle was on either side of the cone plied together = 7.
The hypotenuse is 7, as well as a right triangle, is formed. So:
[tex]\to h^2+r^2 = 49\\\\ \to r^2 = 49-h^2[/tex]
Calculating the volume of the cone:
[tex]V = (\frac{1}{3}) \pi r^2 h \\\\[/tex]
[tex]= (\frac{1}{3}) \pi (49 -h^2) h\\\\= (\frac{1}{3}) \pi 49h -h^3\\\\[/tex]
[tex]V'(h) = (\frac{1}{3}) \pi 49 - 3h^2\\\\[/tex]
Setting the derivative to zero and solving for h^2:
[tex]49-3h^2 = 0 \\\\ h^2 = \frac{49}{3} \\\\ r^2 = 49-\frac{49}{3} \\[/tex]
[tex]= \frac{ 147 -49}{3} \\\\= \frac{98}{3} \\\\[/tex]
Calculating the maximum volume:
[tex]= \frac{1}{3} \pi \frac{98}{3} \frac{7\sqrt{3}}{3} \\\\= \frac{1}{3} \times 3.14 \times 32.66 \times 4.04 \\\\= \frac{1}{3} \times 3.14 \times 32.66 \times 4.04 \\\\= 138.10[/tex]
F(x)=4x 2 +2x+6f, left parenthesis, x, right parenthesis, equals, 4, x, squared, plus, 2, x, plus, 6 What is the value of the discriminant of fff? How many distinct real number zeros does fff have?
Answers
Answer:
Discriminant = -92
the equation has no distinct real numbers
Step-by-step explanation:
Given the function f(x) = 4x^2 + 2x + 6 where;
a = 4, b = 2 and c= 6
The discriminant is expessed as D = b^2 - 4ac
Substitute;
D = 2^2 - 4(4)(6)
D = 4 - 96
D = -92
Hence the discriminant is -92.
Since the discriminant is less than zero i.e D< 0, this shows that the zeros of the equation are not real but complex numbers. Hence, the equation has no distinct real numbers
Answer:
-92 is the discriminant
0 real value 0's
Step-by-step explanation:
explain how a yard foot and inch are related
Answers
Review & Answer:
Measuring with inches will give us inches. If you look at a ruler, inches are about a pinky finger. If 12 inches together, it is called a yard. If 3 feets are together, it is known as a yard foot
There are eleven shirts in your closet, four
blue and seven green. Three of the blue
shirts and one of the green shirts fit well.
The others are too big. You randomly
select a shirt to wear. It is blue or is too
big.
Answers
If -1 is subtracted from 5, what will be the result?
greater than 4
equal to 4
positive, but less than 4
negative
Answers
Answer:
Greater than 4.
Step-by-step explanation:
the answer is 6, and 6 > 4.
Have a good day! God bless! :D
Find the measurement indicated in each parallelogram. Send help pleaseeee
Answers
Answer:
A
Step-by-step explanation:
The opposite sides of a parallelogram are congruent, then
WT = VU = 21.3 → A
A cooking instructor stated that 5 pounds of roast beef is needed to serve 8 people. Based on the instructor's statement, which of the following equations can be used to find r, the number of pounds of roast beef needed to serve 12 people?
Answers
Answer:
r = 5:8
Step-by-step explanation:
5 pound to 8 people
y= 2x +3
y= 4x-3
Is(3,9) a solution of the system?
Choose 1 answer:
A: yes
B: no
Answers
B:yes
Explanation:
Label the point 3 would be x and 9 would be y. Substitute these points into the equation were it corresponds.
Y= 2x+3
9=2(3)+3
9=6+3
9=9
Y=4x-3
9=4(3)-3
9=12-3
9=9
Hope this helps!!
Answer:
A: yes :)
Step-by-step explanation:
Givens: <-->AD is the perpendicular bisector of segment BC AB = 7x+1 AC = 8x-6 BC = 3x + 9 Find: BD
Answers
Answer:
wheres the pic
Step-by-step explanation:
To solve the following system of equations x+3y=6 2x-3y=3 Which of the following steps should be followed ?
Answers
I
3.) Write the equation of the line that passes through (0,3) and (1.-1) in standard form.
Answers
Given:
The points are (0,3) and (1,-1).
To find:
The equation of line passes through these points.
Solution:
Standard form of a line is
[tex]Ax+By=C[/tex]
We know that, if a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The line passes through (0,3) and (1,-1), so the equation of the line is
[tex]y-3=\dfrac{-1-3}{1-0}(x-0)[/tex]
[tex]y-3=\dfrac{-4}{1}(x)[/tex]
[tex]y-3=-4x[/tex]
Adding 4x and 3 on both sides, we get
[tex]4x+y=3[/tex]
Therefore, the standard form of the line is [tex]4x+y=3[/tex].
I need help pls go to my page and answer the finance question it a lot of points.
DON'T ANSWER SOMETHING IGNORANT
Answers
in a circle what is the ratio of the circumference to its diameter
Answers to pick from: A.are B.radious C.volume D.pi
Pleas answer it fast if you dont know it pleas dont answer.
Answers
Answer:
if i remember from last year..
Step-by-step explanation:
Its B. Radius** i think you misspelled it
Choose the graph below that represents the following system of inequalities: (1 point)
y ≥ −3x + 1
y ≤ 1 over 2 x + 3
Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.
Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line.
Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded below the line.
Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded above the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded below the line.
Answers
Answer:
How much
Step-by-step explanation:
What is the solution to m/-7 less than or equal to 14? m Greater than or equal to –2 m Greater than or equal to –98 m Less than or equal to –2 m Less than or equal to –98
Answers
Answer:
b
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
can someone help me please:(
Answers
A field has an area of 64400m^{2} .
Calculate the area of the field. On the map in cm^{2} .
PLEASE HELP ME TO SOLVES IT SOON!
Answers
Answer:
[tex]644,000,000\ cm^2[/tex]
Step-by-step explanation:
[tex]We\ are\ given:\\Area\ of\ the\ map\ in\ m^2=64400\ m^2\\Hence,\ all\ we\ just\ have\ to\ do\ is\ to\ convert\ it\ into\ cm^2.\\Hence,\\Lets\ derive\ the\ formula\ of\ conversion\ from\ m^2\ to\ cm^2\ and\ vice\ versa.\\We\ know\ that,\\1m=100\ cm\\By\ squaring\ both\ the\ sides\ we\ get,\\(1m)^2=(100cm)^2\\Hence,\\1m^2=100^2\ cm^2\\1m^2=10,000\ cm^2\\Just\ in\ case\ you\ wanna\ convert\ cm^2\ to\ m^2,\\1m^2=10,000\ cm^2\\1cm^2=\frac{1}{10,000} m^2\\[/tex]
[tex]Here,\\As\ the\ area\ of\ the\ field\ in\ m^2=64,400\ m^2\\ As\ the\ area\ of\ the\ field\ in\ cm^2=64,400\ m^2*10,000=644,000,000\ cm^2[/tex]
Can somebody plz help answer these questions for the word problem. They have to be correct!!! Thanks
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST :DD
Answers
ANSWER PLSSS!!!!
When is Ann's distance from home increasing? Give a reason to support your answer
Answers
Answer:
when the #8 lines up with he 40
2. Graph the solution to the inequality y < -4/5x + 4
Answers
Answer:
Use DESMOS graphing calculator
Here's the picture for the answer.
Hope this helped :)
Is this correct? If not please correct me!
Answers
What is the measure of arc FLI?
Answers
Answer:
140
Step-by-step explanation:
By inscribed angles, arc FPI = 2<FLI = 2*110 = 220. Since the entire arc of a circle is 360, we know that arc FLI + arc FPI = 360. Solving, we get arc FLI = 360 - 220 = 140.
I hope this helps!
On Thursday, a website received x advertisement orders. On Friday, the website received 8 more advertisement orders than on Thursday. The expression 2x + 8 represents the total number of advertisement orders received over two days.
What does the "+8" mean in the expression 2x + 8?
how many more advertisements were ordered on Friday than Thursday
the number of days
the number of advertisement ordered on Friday
the total number of advertisement on both days
I NEED HELP ASAP PLS
Answers
Answer:
What does the "+8" mean in the expression 2x + 8?
The +8 is the 8 more advertisement orders received on Friday.
It's 8 more than x.
How many more advertisements were ordered on Friday than Thursday
8
The number of days
2
The number of advertisement ordered on Friday
x + 8
The total number of advertisement on both days
2x + 8
Answer:
A
Step-by-step explanation:
I took the test
4. Isabelle takes the bus to work. The bus ride to work costs her $2.50 each time. She could buy a bus pass for a one-time fee of $15.00 and would then only pay $1.00 each time to ride the bus. How many times would she have to take the bus for the cost to be the same?
Answers
Answer:
6 times.
Exclamation:
You can do 15 divided by 2,50 to get you answer, when you do that you get 6.
(The upcoming and this sentence is pre-written and copy and pasted in every brainly question or comment I write or answer.) If this answer helped you please consider giving it brainliest. If my answer was wrong and you got marked wrong for it, I deeply apologize and hope you will forgive me, since everyone makes mistakes sometimes. If you need me to elaborate on my answer or give further explanation on it, please ask and I will do so. If you need to explain your reasoning on your work feel free to use my words- word for word- without crediting me, the answer was made for you anyways! Hope yall learn from my answer and it helps you in the future with assignments, quizzes, test’s, and more!
- •Trix•
( Yes I know my - •Trix• thingy is not my user but it’s what I would change it to if I could but I can't, please address me as Trix while commenting or talking to me here.)
A community is building a new outdoor basketball court. The length of the court is twice the width.
Answers
Answer:
Step-by-step explanation:
The width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.
The problem states that the width of the basketball court (W) can be modeled by the equation:
W(A) = √(A/2)
where A is the area of the court in square feet.
Since the length (L) of the basketball court is twice the width (W), we can express it as:
L = 2W
Now, let's find the expression for the length (L) in terms of the area (A) of the court.
Step 1: Substitute the value of W from the given model into the expression for L:
L = 2 × √(A/2)
Step 2: Simplify the expression:
L = √(4A/2)
L = √(2A)
So, the expression for the length (L) of the basketball court in terms of its area (A) is given by L = √(2A).
To summarize, the width of the basketball court is given by W(A) = √(A/2), and the length is given by L(A) = √(2A). These expressions allow you to calculate the width and length of the court for a given area A in square feet.
To know more about width
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Complete question :- A community is building a new outdoor basketball court. The length of the court is twice the width. The width of the basketball court in feet can be modeled by w(A)= √A/2 where a is the area in square feet of the court.
hello! I need help on these questions, I’ll give brainlist! :)
Answers
Answer:
1] the original perimeter will be multiplied by three.
2} the original area will be multiplied by 9
Step-by-step explanation:
Write the equation of the line shown. Be sure to use the correct variable.
Equation:
Answers
Answer:
y = -9Step-by-step explanation:
As per diagram, y = -9 for any value of x, so it is the line with equation:
y = -9what is the slope of the line
PLSSS HELPPP
Answers
Slope = 1.6
