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
Vedmedyk [2.9K]
1 year ago
6

Let f(x)=x²+kx+4 and g(x)=x³+x²+kx+2k, where k is a real constant.

Mathematics
1 answer:
antoniya [11.8K]1 year ago
7 0

The value of k such that the graph of f and the graph of g only intersect one is equal to 2.

The value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

<h3>How to find the value of the constant k of a system of two polynomic equations</h3>

Herein we have a system formed by two <em>nonlinear</em> equations, a <em>quadratic</em> equation and a <em>cubic</em> equation. Given the constraint that both function must only intersect once, we have the following expression:

f(x) - x² - k · x = 4       (1)

g(x) - x² - k · x = x³ + 2 · k        (2)

x³ + 2 · k = 4

x³ + 2 · (k - 2) = 0

If f and g must intersect once, then the roots must of the form:

(x - r)³ = x³ + 2 · (k - 2)

x³ - 3 · r · x² + 3 · r² · x - r³ = x³ + 2 · (k - 2)

Then, the following conditions must be met: - 3 · r · x² = 0, 3 · r² · x = 0. If x may be any real number, then r must be zero and the value of k must be:

2 · (k - 2) = 0

k - 2 = 0

k = 2

Therefore, the value of k such that the graph of f and the graph of g only intersect one is equal to 2. According to the image attached below, functions f(x) and g(x) intersect at point (x, y) = (0, 4) for k = 2.

To learn more on polynomic functions: brainly.com/question/24252137

#SPJ1

You might be interested in
You have 2.5 pounds of egg whites.
Rufina [12.5K]

Answer:

15

Step-by-step explanation:

38/2.5=15.2

Round it to 15

4 0
3 years ago
Help me and please explain
k0ka [10]

Answer:

4 attendees

Step-by-step explanation:

we can create and equation (x is the amount of attendees) $8 per attendee at a total of $32 is 8x=32 which you divide on both sides getting x=4 or 4 attendees

4 0
3 years ago
The point G(-5, -4) is translated 1 unit left. What are the coordinates of the resulting point, G′?
Lady bird [3.3K]
Worksheet? I need more information on this topic
7 0
3 years ago
Read 2 more answers
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one
ivanzaharov [21]
The right angle up at the number one and the unknown angle down at 2 are corresponding angles. corresponding angles are congruent. therefore angle down by two is a right angle and so the transversal is perpendicu lar to both lines
8 0
3 years ago
Any help is apprenticed!
zloy xaker [14]

Answer:

y=2/3-4x/9

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • Does the graph show a proportional relationship? Explain your conclusion in the workspace provided
    8·1 answer
  • Find the greatest common factor (GCF) for each number set.
    14·1 answer
  • Change 179km to miles. Type a whole number or a decimal. Round to four decimal places as needed.
    9·1 answer
  • can someone help me write a conclusion paragraph? i wrote an essay on why masks and social distancing were effective and I can't
    15·1 answer
  • Hey I need help on this question if you help me 333 envelopesuehwhhegehshdhdgsgsgsgdgdhsgshdhdhdhdhdhdhdhdjdhdhdhdhdhdhdhdhdhdhd
    7·1 answer
  • 1. Solve the following equation by factoring: 4x2 + 12x + 9 = 0
    12·1 answer
  • Please help me with the question below and i will mark you as BRAINLIEST
    10·2 answers
  • How many quarts of pure antifreeze must be added to 8 quarts of a 40% antifreeze solution to obtain a 60% antifreeze solution?
    10·1 answer
  • Which soap deal has the lowest price per ounce?
    5·1 answer
  • Can someone please help me with these questions ?!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!