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
allochka39001 [22]
3 years ago
8

F(x)=9 x^{3} +2x^2-5x+4 and g(x)=5x^3-7x+4. What is f(x)-g(x)? Show all of your steps and write your finial answer in factored f

orm.
Mathematics
1 answer:
olasank [31]3 years ago
7 0

Answer:

{ -0.5 - √2,  0,  -.5 + √2 }

Step-by-step explanation:

Let's rewrite these two functions in a vertical column:

 f(x)=9 x^{3} +2x^2-5x+4

-g(x)=5x^3-7x+4

Now combine (through subtraction) like terms, in order of descending powers of x:

f(x) - g(x) = 4x^ 3 + 2x^2 + 2x

Let's do some preliminary factoring here.  Factor 2x out of each term, obtaining

f(x) - g(x) = 2x(2x^2 + x + 1)

First setting 2x = 0, we find that x = 0 is one solution.

Applying the quadratic formula to 2x^2 + x + 1, we see that a = 2, b = 1 and c = 1.  Then the two roots of this quadratic are:

      -1 plus or minus √(1^2 - 4(2)(1) )        -1 ± √(8)

x = ----------------------------------------------- = ---------------

                         2(1)                                         2

This simplifies to:

      -1 plus or minus √(1^2 - 4(2)(1) )        -1 ± 2√(2)

x = ----------------------------------------------- = ---------------

                         2(1)                                         2

Thus, the roots of f(x) - g(x) are { -0.5 - √2,  0,  -.5 + √2 }

You might be interested in
You can download songs online for $0.99 each. Write an equation relating the total cost (c) to the number of songs (s) you downl
Nookie1986 [14]

Answer:

It would cost $49.50

$0.99 x 50 = $49.50

5 0
3 years ago
What is the slope of the line through (-9,6) and (3,-9)
mrs_skeptik [129]
Answer: the slope is 5/4
step by step explanation: -9-6=-15 3- -9=12
15/12= 5/4
8 0
3 years ago
1. What are the roots of this equation? x2 + 4x + 8 = 0 A. –1 + i B. –4 +1 C. –2 + 21 D. -1 + 4​
Fynjy0 [20]

Answer:

5676656423

Step-by-step explanation:

fgh563453w

4 0
3 years ago
What's 3/6-4/6 and simply your answer
Yuri [45]
Your answer would be -1/6
8 0
3 years ago
Can anyone help me out with this please
musickatia [10]
First, let's factor the equation to make it easier to solve for the intercepts:

f(x) = x² + 12x + 32
f(x) = (x + 8)(x + 4)

To find the x-intercepts of a function, set the y value (f(x)) to 0:

0 = (x + 8)(x + 4)
x = -8, -4

Similarly, to find the y-intercept, set the x values to 0:

f(x) = (0 + 8)(0 + 4)
f(x) = (8)(4)
f(x) = 32

*Note that you can see 32 as the y-intercept in the parabola's original equation
4 0
3 years ago
Other questions:
  • What is the greatest common factor of 40 and 63
    14·2 answers
  • A formula used to convert temperature from C degrees Celsius to F degrees Fahrenheit is F 1.8 •C+32 Find the temperature in degr
    15·1 answer
  • PLEASE ANSWER THIS QUESTION ASAP!!!
    10·1 answer
  • Maxwell bought a new pair of skis for $350. He put $110 down and received a students discount of $30. His mother gave him 1/2 of
    13·2 answers
  • School X and school Y play eacb other in a competition. School X has eight more points than school Y. School X has three times a
    5·2 answers
  • Write the equation of the line that passes through the points (-8,3) and
    9·1 answer
  • Poop I don't know what to do-
    6·1 answer
  • 18. A sports store keeps track of how many skateboards they sell each
    13·1 answer
  • Can yall help me cuz I gotta turn this in in 50 minutes
    13·2 answers
  • Carol says that -520/105 • 16/15 • (-1/2) is less than 2.5 . Do you agree? Explain.
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!