1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kompoz [17]
3 years ago
10

PLEASE HELP ! Find the zeros of the given function.

Mathematics
2 answers:
photoshop1234 [79]3 years ago
4 0

Answer:

-1, 4+i, 4-i

Step-by-step explanation:

x^4- 6x^3 + 2x^2 + 26x + 17

Using the rational root theorem

we see if 1, -1, -17 or 17 are roots

Check and see if 1 is a root

1^4- 6(1^3) + 2(1^2) + 26(1) + 17=0

1-6+2+26+17 does not equal 0  1 is not a root

-1

1^4- 6(-1^3) + 2(1^2) + 26(-1) + 17=0

1 +6 +2 -26+17 = 0

-1 is a root

Factor out (x+1)

(x+1) ( x^3-7x^2+9x+17)

Using the rational root theorem again on x^3-7x^2+9x+17

Checking -1

-1 -7 -9 +17=0

-1 is a root

(x+1) (x+1) (x^2-8x+17)

Using the quadratic on the last

8 ±sqrt(8^2 - 4(1)17)

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

    2

gives imaginary roots

4±i

Dennis_Churaev [7]3 years ago
3 0

Answer:

x = -1, 4 + i, 4 - i

Step-by-step explanation:

Possible rational roots are:

+/- 1, +/- 17

Using trial method:

f(-1) = (-1)⁴ - 6(-1)³ + 2(-1)² + 26(-1) + 17

f(-1) = 0

f(1) = (1)⁴ - 6(1)³ + 2(1)² + 26(1) + 17

f(1) = 40

f(-17) = (-17)⁴ - 6(-17)³ + 2(-17)² + 26(-17) + 17

f(-17) = 113152

f(17) = (17)⁴ - 6(17)³ + 2(17)² + 26(17) + 17

f(17) = 55080

This implies that x = -1 is a root, with multiplicity of 2 or 4

Let the other quadratic factor be g(x)

g(x) = [x⁴ - 6x³ + 2x² + 26x + 17] ÷ (x + 1)²

g(x) = [x⁴ - 6x³ + 2x² + 26x + 17] ÷ (x² + 2x + 1)

g(x) = [x²(x² + 2x + 1) - 8x(x² + 2x + 1) + 17(x² + 2x + 1)] ÷ (x² + 2x + 1)

g(x) = x² - 8x + 17

g(x) = 0

x = [-(-8) +/- sqrt[(-8)² - 4(1)(17)]/2

x = [8 +/- 2i]/2

x = 4 +/- i

You might be interested in
What is the factored form of x^12y^12+1
Margarita [4]

Answer:

Step-by-step explanation:

5 0
3 years ago
PLSSSS HELP<br><br> Which statement is true about the ratios shown?
Fiesta28 [93]

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

despacito

3 0
2 years ago
Read 2 more answers
Rewrite the Cartesian equation y=-3 as a polar equation.
andreev551 [17]

r

sin

θ

=

−

3

Explanation:

Imagine we have a point  

P

with Rectangular (also called Cartesian) coordinates  

(

x

,

y

)

and Polar coordinates  

(

r

,

θ

)

.

The following diagram will help us visualise the situation better:

https://keisan.casio.com/exec/system/1223526375

https://keisan.casio.com/exec/system/1223526375

We can see that a right triangle is formed with sides  

x

,  

y

and  

r

, as well as an angle  

θ

.

We have to find the relation between the Cartesian and Polar coordinates, respectively.

By Pythagora's theorem, we get the result

r

2

=

x

2

+

y

2

The only properties we can say about  

θ

are its trigonometric functions:

sin

θ

=

y

/

r

⇒

y

=

r

sin

θ

cos

θ

=

x

/

r

⇒

x

=

r

cos

θ

So we have the following relations:

⎧

⎪

⎨

⎪

⎩

r

2

=

x

2

+

y

2

y

=

r

sin

θ

x

=

r

cos

θ

Now, we can see that saying  

y

=

−

3

in the Rectangular system is equivalent to say

r

sin

θ

=

−

3

Answer link

Jim G.

May 19, 2018

r

=

−

3

sin

θ

Explanation:

to convert from  

cartesian to polar

∙

x

x

=

r

cos

θ

and  

y

=

r

sin

θ

⇒

r

sin

θ

=

−

3

⇒

r

=

−

3

sin

θ

4 0
3 years ago
Suppose the average tread-life of a certain brand of tire is 42,000 miles and that this mileage follows the exponential probabil
Ahat [919]

Answer: The probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .

Step-by-step explanation:

The cumulative distribution function for exponential distribution is :-

P(X\leq x)=1-e^{\frac{-x}{\lambda}}, where \lambda is the mean of the distribution.

As per given , we have

Average tread-life of a certain brand of tire :  \lambda=\text{42,000 miles }

Now , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles will be :

P(X\leq 65000)=1-e^{\frac{-65000}{42000}}\\\\=1-e^{-1.54761}\\\\=1-0.212755853158\\\\=0.787244146842\approx0.7872

Hence , the probability that a randomly selected tire will have a tread-life of less than 65,000 miles is 0.7872 .

8 0
3 years ago
All tablet computers are on sale for 15% off at Just Tablets.
san4es73 [151]
It would be A:303.45$ because 357-53.55 which would be 303.45$
8 0
3 years ago
Read 2 more answers
Other questions:
  • You have returned from a trip to Europe and still have €200 euro. How much in U.S. dollars should you receive if the exchange ra
    14·1 answer
  • To the nearest tenth of a degree, find the sizes of the acute angles in the 5-12-13 triangle and in the 9-12-15 triangle. This e
    14·1 answer
  • Which fraction is equivalent to -0.06?<br><br> -1/6, -6/10, -3/5, or -3/50
    5·1 answer
  • What’s the slope of y=-7x+5
    6·1 answer
  • A suspension bridge has a cable shaped like a parabola. The bridge is supported by two towers. The towers are meters apart. If t
    8·1 answer
  • -68 times the difference between a number and 11 is equal to the number one plus -94
    8·1 answer
  • Which of these equations, when solved, gives a different value of x than the other three? 9.1 = -0.2x + 10 10 = 9.1 + 0.2x 10 –
    10·2 answers
  • Greg wants to find the median of a set of 9 data items. First,he ordered the items from least to greatest. What should he do nex
    6·2 answers
  • UNIT TEST HELP PLS
    13·1 answer
  • Expand the expression to yield a trinomial of the form <br> ax² + bx + c.<br><br> (2x + 3)²
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!