All categories

3 years ago

Using these complex zeros (1,1,-1/2,2+i,2-i) factor f(x)=-2x^5 +11x^4 -22x^3 +14x^2 +4x -5

1 answer:

7 0

$\bf \begin{cases}
x=1\implies &x-1=0\\
x=1\implies &x-1=0\\
x=-\frac{1}{2}\implies 2x=-1\implies &2x+1=0\\
x=2+i\implies &x-2-i=0\\
x=2-i\implies &x-2+i=0
\end{cases}
\\\\\\
(x-1)(x-1)(2x+1)(x-2-i)(x-2+i)=\stackrel{original~polynomial}{0}
\\\\\\
(x-1)^2(2x+1)~\stackrel{\textit{difference of squares}}{[(x-2)-(i)][(x-2)+(i)]}$

$\bf (x^2-2x+1)(2x+1)~[(x-2)^2-(i)^2]
\\\\\\
(x^2-2x+1)(2x+1)~[(x^2-4x+4)-(-1)]
\\\\\\
(x^2-2x+1)(2x+1)~[(x^2-4x+4)+1]
\\\\\\
(x^2-2x+1)(2x+1)~[x^2-4x+5]
\\\\\\
(x^2-2x+1)(2x+1)(x^2-4x+5)$

of course, you can always use (x-1)(x-1)(2x+1)(x²-4x+5) as well.

You might be interested in

Joe's Ice Cream Shop has 7/8 of a gallon of vanilla ice cream left. They use 1/12 of a gallon of ice cream to make one milkshake

Vadim26 [7]

Answer:

Ten and a Half milkshakes can be prepared from the available amount of ice cream.

Step-by-step explanation:

The total vanilla ice cream = 7/8 gallons

Ice cream used for 1 milkshake = 1/12 gallon

Now, total number of milkshakes possible = $\frac{\textrm{Total availibility of ice cream}}{\textrm{Ice cream used for each milkshake}}$

= $\frac{\frac{7}{8} }{\frac{1}{12} } = \frac{7}{8} \times \frac{12}{1} = 10.5$

Hence ten and a half milkshakes can be prepared from the available amount of ice cream.

8 0

3 years ago

Read 2 more answers

Room temperature is considered to be 70 Fahrenheit. suppose the temperature is 23 Celsius. Is this greater than or less than roo

Thepotemich [5.8K]

Yes its actually 73.4 degrees Fahrenheit

7 0

2 years ago

Idk wat to do.....<br>........

oksano4ka [1.4K]

Answer:

Mean : 95

Median : 85

Mode : 90

Part B : Impossible

Step-by-step explanation:

We can make an equation to find the mean using the first 5 history test scores.

$85=\frac{80+75+90+75+95+n}{6} \\ \\ 85=\frac{415+n}{6} \\ \\ 510=415+n \\ \\ n=95$

So a 95 would be needed to have a mean of 85.

Next, the median.

First, we sort the first 5 history scores from least to greatest.

We get 75, 75, 80, 90, 95.

Since, 80 is the middle value, it will be used in the calculation of the median.

We can make an equation with this.

$82.5=\frac{80+n}{2} \\ \\ 165=80+n \\ \\ n=85$

So a score a 85 would be needed to have a median of 82.5

Thirdly, the mode.

Since 90 is already in the set once, we can just have Maliah score another 90 to make 90 the mode (with the exception of 75 of course).

Finally, Part B.

We can use the equation we had for the first mean calculation but change 85 to 90.

$90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125$

So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.

8 0

3 years ago

Write an equation, and express the product in standard form.

rosijanka [135]

Answer: 3 copies of 5 tenths = 3*0.5 = 1.5

Step-by-step explanation:

Ok, if we have:

"3 copies of a number B"

This is written as:

3*B

And we have that the number B is "5 tenths"

Now, a tenth is the first digit after the decimal point.

Then 5 tenths = 5*0.1 = 0.5

B = 0.5

3 copies of 5 tenths = 3*0.5 = 1.5

7 0

3 years ago

How to solve this problem??

slega [8]

$\frac{2}{3} = \frac{18}{x+5}
$
multiply each side by $x+5$
$\frac{2x+10}{3}=18$
multiply each side by 3

8 0

3 years ago