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
Setler [38]
1 year ago
12

Find all x-intercepts of the function. Express your answer as a list of x-values.

Mathematics
2 answers:
Orlov [11]1 year ago
6 0

Step-by-step explanation:

one thing immediately catches the eye : the factors of the terms in the function follow the powers of 4 :

4⁰, 4¹, 4², 4³

and they are going against the powers of x :

x³ has the factor 4⁰

x² has the factor 4¹

x has the factor 4²

x⁰ has the factor 4³

with that we see that one 0 solution (an x- intercept) is x = 4.

f(4) = 4³ - 4×4² - 4²×4 + 4³ = 4³ - 4³ - 4³ + 4³ = 0

so, the functional expression is

(x-4)(x² + ...)

the other 2 zero solutions are covered by the quadratic term.

to get the quadratic term we divide f(x) by (x-4).

x³ - 4x² - 16x + 64 ÷ x - 4 = x² - 16

- x³ - 4x²

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

0 0 - 16x + 64

- - 16x + 64

----------------------‐--------

0 0

so,

f(x) = (x - 4)(x² - 16)

and as we know

(a² - b²) = (a + b)(a - b)

we get

f(x) = (x - 4)(x + 4)(x - 4) = (x - 4)²(x + 4)

so, x = 4 counts as 2 zero solutions, it is a point, where the curve makes a turn and only touches the x-axis, but does not fully intercept it (in the sense to continue on the other side of the x-axis).

and x = -4 is the third zero solution.

so, the x-intercepts are at x = -4, +4

-Dominant- [34]1 year ago
4 0

Answer:

all x intercepts [-4, 0] [4, 0]

Step-by-step explanation:

x-intercept, i.e. y=0

f(x) = x^3 - 4x^2 - 16x + 64 = 0

(x^3 + 4^3) - 4x^2 - 16x = 0         [FYI, x^3 + y^3 = (x + y)(x^2 - xy + y^2)]

(x + 4)(x^2 - 4x + 16) - 4x^2 - 16x = 0

(x + 4)(x^2 - 4x + 16) - 4x(x + 4) = 0

(x + 4)(x^2 - 4x + 16 - 4x) = 0

(x + 4)(x^2 - 8x + 16) = 0

(x + 4)(x - 4)^2 = 0

x = -4 or 4

all x intercepts [-4, 0] [4, 0]

You might be interested in
Need done asap
Stells [14]

Answer:

transitive property

Step-by-step explanation:

According to transitive property, if there is some relation between a and b by some rule , and then there same relation between  b and c by some rule, then

A and C are related to each other by some rule.

Example:

A = B

B=C

then by transitive property

A=C

As value of A and C are same that is B we can say that A is equal to C whose value is B.

_______________________________________________

Given

a =2z and 2z=b

here both c and b has value equal to Z , Thus, they follow transitive property.

8 0
3 years ago
Which quadrilateral does NOT always have two pairs of parallel sides? A. A Square B. A Parallelogram C. A Trapezoid D. A Rhombus
Yuliya22 [10]
D a rhombus because it dosnt always have congruent sides
4 0
3 years ago
Read 2 more answers
-13x>-26____________
Hitman42 [59]

Answer:

x<2

Step-by-step explanation:

-x>-2

x<2

It's the explanation

3 0
3 years ago
Which is a graph of y=3. - 1?
mixer [17]

Answer:

d

Step-by-step explanation:

7 0
3 years ago
What is the surface area of the triangular prism?
Fofino [41]

Answer:

116.33

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Y and x have a proportional relationship, and y = 7 when x = 2. What is the value of x when y = 21?
    15·2 answers
  • Mr George has $59.75 in his bank account, but then he bought some new ties and some pancakes. After the purchase, he was in debt
    5·1 answer
  • Write and slove a problem involves money that can be solved with multiplication equation.
    9·1 answer
  • The price of one share of Starbucks declined five dollars per day for four days in a row. How much did the price of one share ch
    13·1 answer
  • Which expression is equivalent to the given expression?
    7·2 answers
  • Which of the following is the final step in bisecting a line segment? (5 points)
    10·1 answer
  • Help Determine what kind of event is being described.
    10·2 answers
  • 1. Complete the empty cells in the table below with the correct values. sin theta= sqrt 2/2
    8·1 answer
  • Integrate this y=2x In(x²) at point x=3​
    11·1 answer
  • The slope of a line is 3. The y intercept of the same line is -12
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!