MATHEMATICS MIDDLE SCHOOL

Plot the zeros of the polynomial y = x4 + 3x3 − 27x2 + 13x + 42

Answers

Answer 1
Answer:

Answer:

See explanation

Step-by-step explanation:

Consider the polynomial y=x^4+3x^3-27x^2+13x+42 4th power polynomial function has at most 4 zeros.

Integer zeros can be only among the divisors of 42:

\pm1, \ \pm 2,\ \pm 3,\ \pm 6,\ \pm 7,\ \pm 14,\ \pm 21,\ \pm 42

Check them:

y(1)=1^4+3\cdot 1^3-27\cdot 1^2+13\cdot 1+42=1+3-27+13+42=32\neq 0\n \ny(-1)=(-1)^4+3\cdot (-1)^3-27\cdot (-1)^2+13\cdot (-1)+42=1-3-27-13+42=0\n \ny(2)=2^4+3\cdot 2^3-27\cdot 2^2+13\cdot 2+42=16+24-108+26+42=0\n \ny(3)=3^4+3\cdot 3^3-27\cdot 3^2+13\cdot 3+42=81+81-243+39+42= 0\n \ny(-7)=(-7)^4+3\cdot (-7)^3-27\cdot (-7)^2+13\cdot (-7)+42=2,401-1,029-1,323-91+42= 0

Thus,

y=(x+7)(x+1)(x-2)(x-3)

Zeros are plotted in attached diagram.
Answer 2
Answer:

Answer:

The remainder is 0, so -1 is a zero of the polynomial and x + 1 is another factor: (x − 2)(x + 1)(x2 + 4x − 21). Now factor the remaining polynomial using normal means. The fully factored form is (x − 2)(x + 1)(x + 7)(x − 3), so the zeros of the polynomial are x = 2, -1, -7 and 3.

Step-by-step explanation:

Related Questions

7. y = -x + 1Axis of Symmetry:Vertex:Domain:Range:
What percent of 8x is5x
The division of a whole number N by 13 gives a quotient of 15 and a remainder of 2. Find N
A water cooler holds 4.8 gallons of water. The container is .65 full. How many gallons of water are in the cooler?
Compare the ruler you made to an inch ruler.Describe a how they are alike and how they are different

What is the answer to y=2•2^x

Answers

Answer:

y=4^x

Step-by-step explanation:

Please help answer this question Minni has to buy stickers, erasers, and a pencil. She can only spend $4. A sticker costs $0.35, an eraser costs $0.99, and a pencil costs $0.59. Can Minni buy 2 stickers and 2 erasers? [Use the inequality 0.35x + 0.99y + 0.59 ≤ 4] (1 point) Select one: a. Yes, because the total will be $3.27 b. Yes, because the total will be $1.93 c. No, because the total will be $4.27 d. No, because the total will be $5.93

Answers

Answer:  A

Since you already have an equation just put in how many stickers and erasers she wants to get: 0.35(2)+0.99(2)+0.59≤4.

Then you multiply: .35(2)=.70. .99(2)=1.98.

Then add: .70+1.98+.59=3.27, so yes she can since 3.27 is less than 4 so the answer is A

Answer:

A. yes, because the total will be $3.27

Step-by-step explanation:

0.35x + 0.99y + 0.59 ≤ 4

0.35(2) + 0.99(2) + 0.59 ≤ 4

0.70 + 1.98 + 0.59 ≤ 4

3.27 ≤ 4

Please help me! I'm having trouble solving this! In the △PQR, PQ = 39 in, PR = 17 in, and the height PN = 15 in. Find QR. Consider all possible cases.

Answers

Answer: 44

Step-by-step explanation:

we will find RN and NQ, then add together to give us RQ.

To find RN;

RP= 17 PN = 15 and RN =?

using pythagoras theorem,

adj^2 = hyp^2 - opp^2

RN^2 = RP^2 - PN^2

?^2 = 17^2 - 15^2

?^2 = 17^2 - 15^2

?^2 = 289 - 225

?^2 = 64

? = √64

? = 8

RN=8

To find NQ,

PN = 15 PQ=39 and NQ=?

using pythagoras theorem

NQ^2 = PQ^2 - PN^2

?^2 = 39^2 - 15^2

?^2 = 1521 - 225

?^2 = 1296

? = √1296

? = 36

NQ= 36

RQ = RN + NQ

RQ= 8 + 36

RQ=44

-5(2w+1)=25 how do I solve this problem

Answers

Answer:

Step-by-step explanation:

Divide by - 5

-5(2w + 1) / - 5 = 25 / - 5

2w + 1 = - 5              

Subtract 1 from both sides.

2w + 1 - 1 = - 5 - 1

2w = - 6

Divide by 2

2w/2 = -6/2

w = - 3

-5(2w+1)=25

Multiply both sides by -5

(-5)(2w)=-10w

(-5)(1)=-5

-10w-5=25

Move -5 to the other side. Sign changes from -5 to +5.

-10w-5+5=25+5

-10w=30

Divide by -10 for both sides

-10w/-10=30/-10

w=-3

Answer: w=-3

What is the inequality for the question 3x-2<10

Answers

3x - 2 < 10
3x < 12

x < 4

Can someone please help fast I will mark as brainelist

Answers

Answer:

y= 3x - 1

Step-by-step explanation:

y = mx + c

where m is the gradient

c is the y intercept

hope this helps
Other Questions
-15 + 12x = 5x + 7 -3xSOLVE FOR X
The table shows the outputs y for different inputs x:Input(x) 2 4 6 8Output(y) 1 2 3 4Part A: Do the data in this table represent a function? Justify your answer. (3 points)Part B: Compare the data in the table with the relation f(x) = 3x – 10. Which relation has a greater value when x = 8? (2 points)Part C: Using the relation in Part B, what is the value of x if f(x) = 80? (5 points)PLEASE HELP!!!!!!!!!!!
Show all work and provide necessary descriptions
70% of what number is 35 ?