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
Mekhanik [1.2K]
3 years ago
11

Use the quadratic polynomial x2+x−12 to answer the questions. A: Which summary correctly applies the Fundamental Theorem of Alge

bra to the quadratic polynomial? B: Which statement correctly verifies the application of the Fundamental Theorem of Algebra? Select one answer for question A, and select one answer for question B. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has exactly two roots. B: The quadratic equation x2+x−12=0 has two real solutions, x=3 or x=−4, and therefore has two real roots. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has two or fewer roots. A: This polynomial has a degree of 2, so the equation x2+x−12=0 has more than two roots. B: The quadratic equation x2+x−12=0 has two real solutions, x=−3 or x=4, and therefore has two roots. B: The quadratic equation x2+x−12=0 has one real solution, x=3, and therefore has one real root with a multiplicity of 2.
Mathematics
1 answer:
Murljashka [212]3 years ago
7 0

Answer:

<h3>It can be concluded that this polynomial has a degree of 2, so the equation x²+x−12=0 has exactly two root</h3>

Step-by-step explanation:

Given the quadratic polynomial  x²+x−12, the highest power in the quadratic polynomial gives its degree. The degree of this  quadratic polynomial  is therefore 2. <u>This means that the equation has exactly two solutions. </u>

Let us determine the nature of the roots by factorizing the  quadratic polynomial and finding the roots.

x²+x−12 = 0

x²+4x-3x−12 = 0

= (x²+4x)-(3x−12) = 0

= x(x+4)-3(x+4) = 0

= (x-3)(x+4) = 0

x-3 = 0 and x+4 = 0

x = 3 and -4

This shows that the  quadratic polynomial has <u>two real roots</u>

<u>It can be concluded that this polynomial has a degree of 2, so the equation x²+x−12=0 has exactly two roots</u>

You might be interested in
If 75% of a budget is $270, what is a full budget
Mariulka [41]

Answer:

I think it's 1789 but I'm not completely sure

4 0
3 years ago
An investment of ​$100 comma 000 was made by a business club. The investment was split into three parts and lasted for one year.
Artist 52 [7]

Answer:

  • $54000 was invested at​ 8% interest
  • $36000 was invested at​ 6% interest
  • $10000 was invested at​ 9% interest

Step-by-step explanation:

Total Investment = ​$100,000

The investment was split into three parts (say x, y and z)

  • x+y+z=100000

Simple Interest = Principal X Rate/100 X Time

The first part of the investment earned​ 8% interest

Interest on the first part = 0.08x

The second part of the investment earned​ 6% interest

Interest on the second  part = 0.06y

The third part of the investment earned​ 9% interest

Interest on the third part = 0.09z

Total interest from the investments = $ 7380.

Therefore:

0.08x+0.06y+0.09z=7380

The interest from the first investment was 2 times the interest from the second.

0.08x=2 X 0.06y

0.08x=0.12y

Substituting we have:

0.12y+0.06y+0.09z=7380

0.18y+0.09z=7380

From 0.08x=0.12y

x=1.5y

Substituting x=1.5y into x+y+z=100000

1.5y+y+z=100000

2.5y+z=100000

z=100000-2.5y

Substituting z=100000-2.5y into 0.18y+0.09z=7380

0.18y+0.09(100000-2.5y)=7380

0.18y+9000-0.225y=7380

-0.045y=-1620

Divide both sides by -0.045

y=36000

Recall: x=1.5y

x=1.5 X 36000

x =54000

x+y+z=100000

54000+36000+z=100000

z=100000-(54000+36000)

z=10,000

Therefore:

  • $54000 was invested at​ 8% interest
  • $36000 was invested at​ 6% interest
  • $10000 was invested at​ 9% interest
3 0
3 years ago
The volume of a cube is 2197mm (cubed) what is the length of its side
Mademuasel [1]

Answer:

l^3=volume of cube

l^3=2197

l=13

5 0
3 years ago
Please answer!(20pts) Each month your parents deposit $75 into your college fund. The account pays an annual rate of 3.5% compou
balandron [24]
I’m not quite sure but i need to help someone
8 0
2 years ago
The graph shows the relationship between mass and volume for pure silver. Use the graph to determine the density of pure silver
Natalija [7]

Answer:

C. Slope and 10.49 g/cm^3

Step-by-step explanation:

We're missing the graph itself, but I can make an educated guess:

- Assuming x = volume and y = mass:

p = \frac{m}{v}

density = mass/volume

x = volume = run

y = mass = rise

mass/volume = rise/run = slope

The slope of the line (assuming the graph is purely linear) represents mass/volume, which is the formula for density.

I had to Google the density of silver itself. Do the math from the graph for a more appropriate answer, as the graph may be less scientifically precise.

7 0
3 years ago
Other questions:
  • What is equivalent to 3x - 4y = 6
    6·2 answers
  • Right Isosceles Triangle ABC has a hypotenuse of length h. Line segment DE is a midsegment with length 4x. What is the perimeter
    14·1 answer
  • Please help me and hurry
    5·1 answer
  • Will give brainliest answer
    9·2 answers
  • Lisa, an experienced shipping clerk can fill an order in 9 hours. Felipe a clerk needs 11 hours to do the same job. Working toge
    13·1 answer
  • Which is the correct algebraic expression after combining like terms? 6 c d + 3 c minus 7 d minus 3 c d + 4 d + one-third c 3 c
    14·2 answers
  • How many lines of reflective symmetry and how many centers of rotational symmetry does the parallelogram depicted below have?
    7·1 answer
  • Answer this question: -12d- 6= -2(d+3)- 10d
    11·2 answers
  • If an item that originally cost $20 is increased to $27, what is the percentage of increase in the item?
    12·2 answers
  • A local school district requires all fourth graders to complete a 20-minute test containing 200 multiple-choice mathematics prob
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!