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Sphinxa [80]
3 years ago
14

Find the roots of the polynomial equation.

Mathematics
2 answers:
raketka [301]3 years ago
7 0
Set f(x) = x³ - 2x² + 10x + 136.

Use Descartes' rule of signs.
f(x) has 2 change in sign, so there are
(1) 2 real roots, or
(ii) a pair of conjugate imaginary roots.

f(-x) = -x³ - 2x² - 10x + 136
f(-x) has 1  sign change so there is 1 real root. 

Scan the function for the first zero crossing, using negative values of x.

 x    f(x)
--- ---------
-1   123
-2  100
-3    61
-4      0

x = -4 is a root, so (x+4) is a factor.
Perform synthetic division (or long division if you do not know synthetic division).

 
-4 |  1  -2  10  136
          -4  24 -136
    ---------------------
       1  -6  34      0

Therefore
f(x) = (x+4)(x²- 6x + 34) = 0

Before factoring x² - 6x + 34, test the discriminant.
D = (-6)² - 4*34 = -100 => we have a pair of imaginary roots.
Use the quadratic formula.
x = (1/2)[6 +/- √-100]
   = 3 +/- 5i

Answer: C
The roots are -4, 3 +/- 5i
Luden [163]3 years ago
6 0

The answer (Which is 3 +/- 5i, -4) is now B on the Unit 6 Test.


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Elanso [62]

Replace the x in 7x by (3x + 1):-

(f o g)(x) = 7 * (3x + 1)

= 21x + 7   which is choice D.

3 0
3 years ago
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Dimas [21]

The linear function that describes Juan's elevation during his descent is:

B. y = -1460x + 7500.

<h3>What is a linear function?</h3>

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

In this problem, each hour, the height decays by 1460, hence the slope is of m = -1460, then:

y = -1460x + b.

The y-intercept is found considering that when x = 1, y = 6040, hence:

b = 6040 + 1460 = 7500.

Which means that option B is correct.

More can be learned about linear functions at brainly.com/question/24808124

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2 years ago
A group of college students developed a solar-powered car and entered it in a race. The car travels at a constant speed of 100 m
nekit [7.7K]

Answer:

A) Distance time graph

B) d(t) = 25t

C) The expression shows the distance more clearly.

Step-by-step explanation:

A) A distance time graph as seen in the attachment provides a representation of the distance travelled.

We are told the car travels at a constant speed of 100 meters per 4 seconds. Which means that 100 m for each 4 hours. So, for 200m, it's 8 hours like seen in the graph and for 300m,it's 12 hours as seen in the graph.

B) And expression for the distance is;

d = vt

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d is distance in metres

v is speed in m/s and t is time

We are told that the car travels at a constant speed of 100 meters per 4 seconds.

Thus, v = 100/4 = 25 m/s

Distance travelled over time is;

d(t) = 25t

C) Looking at both A and B above, it's obvious that the expression of the distance shows a more clearer way of getting the distance because once we know the time travelled, we will just plug it into the equation and get the distance. Whereas, for the representation form, one will need to longer graphs if the time spent is very long.

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Answer:

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