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avanturin [10]
3 years ago
5

Write an equation for the polynomial function that has 2 and -3 + 5i as zero

Mathematics
1 answer:
AysviL [449]3 years ago
8 0

Answer:

p(x) = {x}^{3}  + 4{x}^{2}  + 22x- 68

Step-by-step explanation:

We want to write an equation for the polynomial function with roots;

x = 2

and

x =  - 3 + 5i

Note that complex roots come in pairs and in conjugates.

Therefore

x =  - 3 - 5i

is also a root.

By the factor theorem:

(x-2), (x+3+5i), and (x+3-5i) are factors of the polynomial.

Let p(x) be the polynomial, then in factored form.

p(x) = (x - 2)(x + 3 + 5i)(x + 3 - 5i)

We expand now to get:

p(x) = (x - 2)( {x}^{2}  + 3x  -  5ix + 3x + 9 - 15i + 5ix + 15i + 25)

Simplify now

p(x) = (x - 2)( {x}^{2}  + 6x +34)

We expand further;

p(x) = x( {x}^{2}  + 6x + 34) - 2( {x}^{2}  + 6x + 34)

p(x) = {x}^{3}  + 6 {x}^{2}  + 34x - 2 {x}^{2}   - 12x  - 68

p(x) = {x}^{3}  + 4{x}^{2}  + 22x- 68

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Solve the following word problem using any method. Show your work.
VLD [36.1K]
Let's set up two equations:
x+y=20             We know she brought total of 20, some of each so x=small y=big
20x+ 30y=450
 
 x+y= 20
   -y    -y
 ------------
 x= 20 -y

substitute into the other equation:    
20 (20-y) + 30y = 450
400 - 20y + 30y = 450
400+ 10 y = 450
10 y = 50
y= 5

So she brought  5 big cases.  Then substitute the value of y into one of the equations.

5+ x = 20 
x= 15

So we bought 15 small cases and 5 big cases. 

Hope this helps! Please give me the brainliest answer if you like it! If you have further questions, please leave a comment or add me as a friend!


5 0
3 years ago
Read 2 more answers
Step by set
Roman55 [17]

Answer:

2 2/3 or 8/3

Step-by-step explanation:

Step by step I am guessing? (Is that what each question is for?)

STEP 1

First we have to find 1/3 of 23:

23/3= 1/3 of 23

Then:

5/1 = 15/3

STEP 2

Subtract:

23-15= 8/3

8/3 or 2 2/3

3 0
3 years ago
Simplify sin^2y/sec^2 y−1 to a single trigonometric function
liubo4ka [24]

Answer:

\frac{ { \sin}^{2} y}{ { \sec}^{2}y - 1 }  =  { \cos }^{2} y

Step-by-step explanation:

We know that { \tan }^{2} y =  { \sec }^{2} y - 1

Also , { \tan}^{2} y =   \frac{ { \sin }^{2} y}{ { \cos }^{2}y }

So ,

\frac{ { \sin }^{2}y }{ { \sec }^{2}y - 1 }  =  \frac{ { \sin}^{2} y}{ { \tan }^{2} y}  =  \frac{ { \sin }^{2}y }{ \frac{ { \sin}^{2} y}{ { \cos}^{2}y } }  =  { \cos }^{2} y

6 0
2 years ago
M
Ierofanga [76]

Answer:

see below

Step-by-step explanation:

m/3 + 4 = 7

Subtract 4 from each side

m/3+4-4 = 7-4

m/3 = 3

Multiply each side by 3

m/3*3 = 3*3

m =9

4 0
3 years ago
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UkoKoshka [18]

Answer:

Answer: B

Step-by-step explanation:

5 Inches × 6 Inches

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