Given:
Zeroes of a polynomial are –2, –4, –3 + 4i.
To find:
The polynomial function of least degree with real coefficients in standard form.
Solution:
According to the complex conjugate root theorem, if a complex number a+ib is a zero of a polynomial, then its conjugate a-ib is also a zero of than polynomial.
–3 + 4i is zero of the polynomial. So, by complex conjugate root theorem -3-4i is also a zero of required polynomial.
If c is a zero of p(x), then (x-c) is a factor of p(x).
–2, –4, –3 + 4i, -3-4i are zeroes of the polynomials. So, (x+2), (x+4), (x+3-4i), (x+3+4i) are the factors of the required polynomial.
Let the required polynomial be p(x), so
[tex]p(x)=(x+2)(x+4)(x+3-4i)(x+3+4i)[/tex]
[tex]p(x)=(x^2+4x+2x+8)((x+3)^2-(4i)^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16i^2)[/tex] [tex][\because (a+b)^2=a^2+2ab+b^2][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9-16(-1))[/tex] [tex][\because i^2=-1][/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+9+16)[/tex]
[tex]p(x)=(x^2+6x+8)(x^2+6x+25)[/tex]
[tex]p(x)=x^2(x^2+6x+25)+6x(x^2+6x+25)+8(x^2+6x+25)[/tex]
[tex]p(x)=x^4+6x^3+25x^2+6x^3+36x^2+150x+8x^2+48x+200[/tex]
Combining like terms, we get
[tex]p(x)=x^4+(6x^3+6x^3)+(25x^2+36x^2+8x^2)+(150x+48x)+200[/tex]
[tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex]
Therefore, the required polynomial is [tex]p(x)=x^4+12x^3+69x^2+198x+200[/tex].
Plz help me on this
Andrews sandwich consists of a 20 g piece of cheese is 60 g piece of turkey into 30 g slices of bread what is the total weight of Andrews sandwich in kilograms
Answer:
0.11 kilos
Step-by-step explanation:
PLEASE HELP MEE, IM STUCK
Answer:
im pretty sure its c
if this helped please consider giving brainliest
Suppose the newspaper states that the probability of rain today is 50%. What is the complement of the event "rain today"?
Answer:
50%
Step-by-step explanation:
Given that :
Let Probability of rain today = P(rain today) = 50% = 0.5
The complement of an event A denoted as A' means the opposite of event A is obtained by subtracting event a from 1.
P(rain today) = 0.5
The complement of P(rain today) ; means the probability that it will NOT rain today;
Hence, P(raintoday') = 1 - 0.5 = 0.5 = 50%
Find the 52nd term.
-4, -1, 2, 5, ...
a52=46
a52=47
a52=149
a52=44
Answer:
149
Step-by-step explanation:
- 4, - 1, 2, 5, ...
[tex]a_{1}[/tex] = - 4
d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = - 1 - (- 4) = 3
[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d
[tex]a_{52}[/tex] = - 4 + (52 - 1)(3) = 149
5x + 24 + 5(x + 5)
HELP FAST
5x+24+5(x+5)
Distribute:
=5x+24+(5)(x)+(5)(5)
=5x+24+5x+25
Combine Like Terms:
=5x+24+5x+25
=(5x+5x)+(24+25)
=10x+49
Answer:= 10x+49
solve for x
10x =-49
10/10x -49/10
x= -4.9
Hope this helps
expand and simplify (x+1)(x+7)
Answer:
Factored?
x^2 + 8x +7
Step-by-step explanation:
x times x = x^2, with 7 times x = 7x and x times 1 = 1x. Add those two common terms together to get 8x. Then lastly 7 times 1 =7 so add that.
Simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
What is simplification?
"Simplification in mathematics means to write the given expression in such a way that it is easy to understand."
According to the question,
Simplify the given equation by opening the brackets we get,
(x + 1)(x + 7)
= x² + 1x +7x +7
= x² + 8x + 7
Hence, simplify form of (x + 1)(x + 7) is equals to x² +8x +7.
Learn more about simplification here
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What is the ratio of the number of beaks to the number of legs the chickens and the sheep have on this farm?
Number of Chickens Number of Sheep
8 14
1 to 9
because 1 chicken has 1 beak so the ratio of beaks is 8
1 sheep has 4 legs while 1 chicken has 2 legs
therefore multiply 4legs by 14 =56 then multiply 2 legs by 8=16
Beaks Legs
8. 72
1. 9
th ratio is therefore 1 : 9
A farmer wants to fence off part of a rectangular field to create an area that is 22,500 square feet. He then wants to divide that area in half by creating a fence parallel to one side of the rectangle. Find the dimensions of the area that will minimize the amount of fencing he needs.
Answer:
90 x 125
Step-by-step explanation:
22500÷2 = 11250
factors of 11250 = {1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 125, 150, 225, 250, 375, 450, 625, 750, 1125, 1250, 1875, 2250, 3750, 5625, 11250} (this took me long to type and calculate lol)
well we want the factors as close as possible to minimize the perimeter. In this case, it is 90 and 125. therefore the dimenstions are 90 x 125
PLEASE HELP WORTH 30 POINTS
Answer
You have a common factor of 10 You have a common factor of 5 You have a common factor of 15/2 You have a common factor of 4Find the measure of the indicated side. Round to the nearest tenth.
Answer:
x=23.5
Step-by-step explanation:
[tex]cos59.3=\frac{12}{x}\\x(cos59.3)=12\\x=\frac{12}{cos59.3}\\x=23.5[/tex]
Bobby wants a PS5. Best Buy is selling them at 35% off. Their regular price is $500.00. Walmart is offering then at 45% off of their normal price $600.00. Where will Bobby get the best deal? Explain your answer and reasoning using complete sentences.
Answer:
Walmart I hope this helps!!
Step-by-step explanation:
What is the answer to this question?
the measure of an angle is 168°. what is the measure of its supplementary angle?
Answer:
Im not sure but I think its 12
Step-by-step explanation:
Please Help Me!!! I'm Being Timed!!! What is -2(3x+12y-5-17x-16y+4) simplified?
Answer:
28x + 8y + 2 hope that helps
Tell whether the sequence is arithmetic. If it is, identify the common difference. 4, 8, 16, 32, …
Answer:
it's geometric
8/4=2 16/8=2
d=2
A bag of flour contains 24 cups. Each sponge cake that Gilda makes uses 3 cups of
flour. How many cakes can she make with one bag of flour?
8
3
24
1
Answer:
8
Step-by-step explanation:
This is the answer because:
1) Since there are 24 cups in one bag and she uses 3 cups per cake, all we have to do is divide:
24 ÷ 3 = 8
Therefore, the answer is 8.
Hope this helps! :D
Which equation can be used to solve for c? Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c. c = (5)cos(35o) c = Start Fraction 5 Over cosine (35 degrees) End Fraction c = (5)sin(35o) c = Start Fraction 5 Over sine (35 degrees) End Fraction
Answer:
it is B because the teacher gave me the answer hope y'all enjoy
Step-by-step explanation:
a store has 5 cans of soup for 15 dollars.How much is per can
Answer:
3 dollars
Step-by-step explanation:
5 cans= 15 dollars
1 can = 15/5= 3
3 dollars
What is the solution to the inequality x(x - 3) > 0?
OA) xs O and x > 3
OB) xs O or x3
OC) 0
OD) x<0 or x> 3
Answer:
D) x<0 or x>3
Step-by-step explanation:
x(x-3)>0
either x>0 and x-3>0 .... positive-positive=positive so x>3
or x<0 and x-3<0 ..... negative-negative=positive so x<0
if x=0 then x(x-3)=0
The solution to the inequality is x < 0 or x > 3
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
To solve the inequality x(x - 3) > 0, we can use a sign chart.
First, we can find the critical points of the inequality, which are the values of x that make the expression x(x - 3) equal to zero. These values are x = 0 and x = 3.
Then, we can create a sign chart with these critical points and test intervals between them to determine the sign of the expression x(x - 3) in each interval.
Interval Test Value x(x - 3)
x < 0 -1 Positive
0 < x < 3 1 Negative
x > 3 4 Positive
From the sign chart, we see that x(x - 3) is positive when x < 0 and when x > 3, and negative when 0 < x < 3.
Hence , the solution to the inequality x(x - 3) > 0 is x < 0 or x > 3
To learn more about inequality click :
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.Solve for x in the equation below:
x1/2- 4 = 8
Answer:
x = 144
Step-by-step explanation:
[tex] x^\frac{1}{2} - 4 = 8 [/tex]
Add 4 to both sides.
[tex] x^\frac{1}{2} = 12 [/tex]
Square both sides since x^(1/2) is the same as sqrt(x).
[tex] (x^\frac{1}{2})^2 = (12)^2 [/tex]
[tex] x^{\frac{1}{2} \times 2} = 144 [/tex]
[tex] x^1 = 144 [/tex]
[tex] x = 144 [/tex]
3/4 =w/6 simplify as much as possible HELP plzzz
Answer:
9/2
Step-by-step explanation:
3/4 = w/6
w = 3/4 *6
w = 9/2
Laura is graphing an absolute-value function in the form
f(x) = a|x - h| +k. She determines that the domain
is (-00,00) and that the minimum value is y=-3.
What might be the equation of this function?
A. f(x) = \x + 3) + 3
B.f(x) = -3\x+31 - 3
C.f(x) = (x – 31 - 3
D.f(x) = 3|x – 3] + 3
Answer:
The equation of the function is;
y = |x-3| -3
Step-by-step explanation:
Here, we want to give the absolute-value function
For the minimum value to be -3, it means that k is negative
since the domain is the set of all real numbers, then we do not have any undefined value for the range y
So, the equation is ;
y = |x-3| - 3
11r - 14r - 3 + 16 what is the answer
Answer:
-3r + 13
Step-by-step explanation:
11r - 14r - 3 + 16
add like terms
-3r + 13
y= [ ? ]
PLEASE HELP
Answer:
Step-by-step explanation:
it's a 90° angle .. : )
Answer:
Step-by-step explanation:
2x + 70 = 110
2x = 110 - 70
x = 20
y = x+70
y = 20+70 = 90
Jose is 49 inches tall. His mother is 18 inches taller. How tall is Jose's mother?
67 inches or 5.58 feet.
A 6 foot tall tent standing next to a cardboard box casts a 9 foot shadow. If a cardboard box cast a shadow that is 6 feet long then how tall is
Answer:
It is 4 feet tall
Step-by-step explanation:
Filler
Given the measures of the sides of a triangle below, which set could form a right
triangle?
A. 6, 7, 8
B. 9, 12, 15
C. 12, 15, 20
D. 20, 25, 30
(give a brief explanation please)
A number times nine + four gives you fifteen if you have time
Answer:
11 / 9
Step-by-step explanation:
Let number = x
(x * 9) + 4 = 15
9x + 4 = 15
9x = 15 - 4
9x = 11
x = 11 / 9
Hence, the number is 11 /9
100 points explaination
Answer: bro I'm sorry I don't know how to help you please give me points
Step-by-step explanation:
Don't know how to help you sorry
Answer: okay, this brother.
Step-by-step explanation: