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3 years ago

Isabel finished her English assignment in

Mathematics

1 answer:

defon3 years ago

6 0

Answer:

52 minutes

Step-by-step explanation:

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Find number a and k so that x-2 is afactor<br>OF F(x)=x4-2ax tax-<br>X+k and F(-1)=3

Slav-nsk [51]

Question:

Find numbers a and k so that x-2 is a factor of

$f(x)=x^4-2ax^3+ax^2- x+k$

and

$f(-1)=3$

Answer:

$k = -2$ and $a=1$

Step-by-step explanation:

Given

$f(x)=x^4-2ax^3+ax^2- x+k$

$Factor:\ x - 4$

$f(-1)=3$

Required

Find a and k

For $f(-1)=3$

Substitute -1 for x

$f(x)=x^4-2ax^3+ax^2- x+k$

$f(-1) = (-1)^4 - 2a *(-1)^3 + a*(-1)^2 - (-1) + k$

$f(-1) = 1 - 2a *-1 + a*1 +1 + k$

$f(-1) = 1 +2a + a +1 + k$

$f(-1) = 2 +3a + k$

Substitute 3 for f(-1)

$3 = 2 +3a + k$

Collect Like Terms

$3 - 2 = 3a + k$

$1 = 3a + k$

Also:

If $x - 2$ is a factor, then

$f(2) = 0$

Substitute 2 for x and 0 for f(x)

$f(x)=x^4-2ax^3+ax^2- x+k$

$0 = 2^4 - 2a * 2^3 + a * 2^2 - 2 + k$

$0 = 16 - 2a * 8 + a * 4 - 2 + k$

$0 = 16 - 16a + 4a - 2 + k$

$0 = 16 - 12a - 2 + k$

Collect Like Terms

$2 - 16 = - 12a + k$

$-14 = k - 12a$

$k = 12a - 14$

Substitute 12a - 14 for k in $1 = 3a + k$

$1 = 3a + 12a - 14$

$1 = 15a - 14$

Collect Like Terms

$15a = 1 + 14$

$15a = 15$

Solve for a

$a = \frac{15}{15}$

$a=1$

Substitute 1 for a in $k = 12a - 14$

$k = 12 * 1 - 14$

$k = 12 - 14$

$k = -2$

3 0

2 years ago

PLEASE HELP ASAP IL MARK BRAIN....

fenix001 [56]

I’m pretty sure it is a

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3 years ago

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Postal Packages shipped a total of 120 packages last week, and 24 of them were shipped internationally. What percent of the pack

dsp73

Answer:20% OF THEM WERE SHIPPED INTERNATIONALLY IT IS THE BLUE MODEL NOT THE PINK ONE

Step-by-step explanation:

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3 years ago

60% of a number is 90 what is the number?

kramer

Answer:

The number is 150

Step-by-step explanation:

Is means equals and of means multiply

60 % * N = 90

.60 N = 90

Divide each side by .6

N = 90/.6

N =150

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2 years ago

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Is g(x)=4+x^2/1+x^4 even, odd or neither

UkoKoshka [18]

Since g(-x) is equal to g(x), the function is an EVEN FUNCTION.

<h3>Is the given function even, odd or neither?</h3>

Given the function in the question;

g(x) = (4 + x²)/(1 + x⁴)

To determine if the function is even, odd or neither, we find g(-x) by substituting -x for all occurrence of x in the function.

g(x) = (4 + x²)/(1 + x⁴)

g(-1) = (4 + (-x)²)/(1 + (-x)⁴)

Simplify

g(-x) = (4 + x²)/(1 + x⁴)

Hence,

g(-x) = g(x)

Since g(-x) is equal to g(x), the function is an EVEN FUNCTION.

Learn more about even functions here: brainly.com/question/23446734

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2 years ago