MATHEMATICS MIDDLE SCHOOL

Which of the following quartic functions has x=-1 and x = -2 as its only two real zeros?
Which of the following quartic functions has x=-1 and x - 1

Answers

Answer 1
Answer:

Answer:

Equation 3

Step-by-step explanation:

Lets see which of the functions has -2 as a zero root. We will go in order:

(1) (-2)^4 - 3(-2)^3 + 3(-2)^2 -3(-2) + 2 = 16 - 3(-8) + 3(4) + 6 +2 = 16 +24 +12 + 6 +2 =60 >0

So, (1) is wrong!

(2) (-2)^4 + 3(-2)^3 + 3(-2)^2 - 3(-2) - 2 = 16 - 24 + 12 + 6 - 2 =34 - 26 = 8 > 0

(2) is also wrong!

(3) (-2)^4 + 3(-2)^3 + 3(-2)^2 +3(-2) + 2 = 16 - 24 + 12 - 6 + 2 = 30 -30 = 0

The zero root x=-2 fits, what about x=-1?

(-1)^4 + 3(-1)^3 + 3(-1)^2 +3(-1) + 2 = 1 - 3 + 3 - 3 + 2 = 6 - 6 = 0

So, equation (3) fits both!

Finally, lets see (4):

(-2)^4 - 3(-2)^3 - 3(-2)^2 + 3(-2) + 2 = 16 + 24 - 12 - 6 + 2 = 42 - 18 = 24 > 0

So, (4) is also wrong.

Only equation 3 fits both zero roots!
Answer 2
Answer:

Final answer:

The quartic function with x=-1 and x=-2 real roots is x^4+6x^3 +12x^2+12x+4. Quartic functions are polynomial functions of degree 4; quadratic equations resources also help understand the concept. In essence, finding roots of quartic functions follow the same logic as that of quadratic functions.

Explanation:

The subject matter pertains to quartic functions in mathematics. Quartic functions are polynomial functions with a degree of 4. From the question, the given zeros are x=-1 and x=-2, having multiplicity of 2 each (since there are only two real zeros). Thus, the quartic function with these zeros will be (x+1)^2*(x+2)^2. This can be expanded to x^4+6x^3 +12x^2+12x+4.

Exemplifying the relevance of The Solution of Quadratic Equations, normally known as second-order polynomials or quadratic functions, such equations can also be used to find zeros of the functions when set to equal zero. In this scenario, quartic functions are a degree higher, but the same principle applies in finding the roots when the equation is set equal to zero.

Learn more about Quartic Functions here:

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Solve for x.
−7.8(x+6.5)=−25.74
Enter your answer, as a decimal, in the box.

Answers

−7.8(x+6.5)=−25.74
-7.8x - 50.7 = -25.74
-7.8x = -25.74 + 50.7
-7.8x = 24.96
      x = 24.96/-7.8
      x = -3.2

A gardening box has a perimeter of 27 1/2 feet. if the length is 9 feet, what is the area?

Answers

42 ³/₄ ft²

Further explanation

Given:

  • A gardening box has a perimeter of 27 ¹/₂ feet.
  • The length is 9 feet.

Question:

What is the area?

The Process:

A gardening box is rectangular. Units of length that are the same, i.e., in feet.

The perimeter formula is as follows:

\boxed{ \ Perimeter = length + length + width + width \ }

It can also be written as follows:

\boxed{\boxed{ \ Perimeter = 2 * (length + width) \ }}

Step-1: calculate the width

Let's use the formula above.

\boxed{ \ 2 * (9 + width) = 27(1)/(2) \ }

\boxed{ \ 9 + width = (55)/(2) / 2 \ }

\boxed{ \ 9 + width = (55)/(2) * (1)/(2) \ }

\boxed{ \ 9 + width = (55)/(4) \ }

\boxed{ \ width = (55)/(4) - 9 \ }

\boxed{ \ width = (55)/(4) - (36)/(4) \ }

\boxed{\boxed{ \ width = (19)/(4) \ ft\ }}

Step-2: calculate the area

The area formula is as follows:

\boxed{\boxed{ \ Area = length * width \ }}

\boxed{ \ Area = 9 * (19)/(4) \ }

\boxed{ \ Area = (171)/(4) = 42(3)/(4) \ }

Thus, the area of a gardening box is\boxed{\boxed{ \ 42(3)/(4) \ ft^2 \ }}

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Keywords: a gardening box, has a perimeter, 27 1/2 feet, the length, width, 9 feet, what is the area?, rectangular, formula
To figure out the width is easy all you do is subtract the length twice, because of there being 2 sides that have the same length,and then divide whatever is left. So its 27.5-18=9.5. 9.5/2=4.75. 4.5 is your width. and now area. area=length times width, so a= 9 times 4,75, which is 42.75.

Is 6xyz and 8xy like terms

Answers

you can combine variables that are the same such as 6x and 8x, and y and y. that would end up being 14x+2y+z

What expression shows the relationship between the value of any term and n, its position in the sequence for the given sequence?2, 1, 0, -1, -2, ...
A) 2n
B) n + 3
C) 2n + 1
D) -n + 3

Answers

The answer is obviously B

Answer:The answer is D

Step-by-step explanation: for the first term (1)

-(1)+3=2. Whist is the correct number for the 1st term

Which explicit formula
-8, -5, -2, 1, 4,...

Answers

Answer:

then 7,10,13 and so one so forth

Step-by-step explanation:

you are subtracting three as you go on.

Simplify the complex fraction. Please show all work!

Answers

Answer:

3(u^2 +u-3)

-------------------

u(u-3)^2

Step-by-step explanation:

u         1

---- + -------

u-3      u

-------------------------

    u-3

  ----------

    3

Get a common denominator for the numerator

u *u         1(u-3)

----      + -------

(u-3)u      u(u-3)

-------------------------

    u-3

  ----------

    3

u *u + (u-3)

-----------

(u-3)u      

-------------------------

    u-3

  ----------

    3

Now use copy dot flip

u *u + (u-3)        3

----------------- * -------------

(u-3)u                 u-3

3(u^2 +u-3)

-------------------

u(u-3)^2
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