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
OlgaM077 [116]
3 years ago
7

Use synthetic division to find the value of p and q if x+1 and x-2 are the factors of x3+ px2 + qx + 6

Mathematics
2 answers:
Vesnalui [34]3 years ago
7 0
A slightly different method: Using the polynomial remainder theorem, you have

x^3+px^2+qx+6\bigg|_{x=-1}=-1+p-q+6=0\implies p-q=-5
x^3+px^2+qx+6\bigg|_{x=2}=8+4p+2q+6=0\implies 2p+q=-7

Adding these equations together, you get

(2p+q)+(p-q)=-12\implies 3p=-12\implies p=-4
p-q=-5\implies -4-q=-5\implies q=1
saveliy_v [14]3 years ago
5 0
Set up synth. div. in the usual way.  If x-2 is a factor of the given polynomial, use +2 as the divisor in synth. div.:
    ______________________________
2 /  1            p                 q                 6

    _______+2______2p+4____________________
       1         p+2        2p+q+4

Finish this.  Note that if 2 is a root and x-2 is a factor, the final result MUST equal 0.  Thus, we get the equation p-q=5.

Do the same thing for the root -1 (which comes from the factor (x+1).

You'll end up with two linear equations which can be solved for p and q.

Substitute these values of p and q into the given polynomial.  p=-4, so that polynomial becomes          x^3 - 4x + q + 6.


I did this, and found that -1 and +2 are indeed roots of the resulting polynomial.
You might be interested in
WHO WANTS TO TALK 2DAY>>> sum1 hmu plz
miss Akunina [59]

Answer:

hi

Step-by-step explanation:

What do you use Phone no. Hi what

4 0
3 years ago
Read 2 more answers
(3x + 10y 2-20<br> { 3x + 2y &gt; 4
dmitriy555 [2]

Answer:

Multiply each equation by the value that makes the coefficients of

x

opposite.

(

−

3

)

⋅

(

2

x

+

5

y

)

=

(

−

3

)

(

20

)

(

2

)

⋅

(

3

x

−

10

y

)

=

(

2

)

(

37

)

Step-by-step explanation:

8 0
3 years ago
The product of two positive numbers is 48. the larger number is 13 more than the smaller. Find both numbers [Only an algebraic s
Valentin [98]

Answer:

Larger number:

16

Smaller number

3

Step-by-step explanation:

Larger number: 16

Smaller number: 3

Explanation:

Suppose the larger number is

a

and the smaller number is

b

.

You solve the following system of equations:

a⋅b=48

a−13=b

Since b is a −13, you can plug that into a⋅b=48, so...a⋅(a−13)=48

a 2−13a=48

a2−13a−48=0

Factor the polynomial:

(a−16)(a+3)=0

a=16 or a=−3a is positive so a=16.

We can now solve for b by plugging in a, so...16−13=b3=b We have a=16 and b=3, meaning that the larger number is 16 and the smaller number is 3.

5 0
3 years ago
5/6 but if i mulsiply by 4 it gives me whole diff
miskamm [114]

Answer:

3.33 or 3 1/3

Step-by-step explanation:

You're correct to multiply by 4.

Your answer will be 10/3

Just make it a mixed number: 3 1/3

3.33 is 10/3 as a decimal.

4 0
2 years ago
A card is selected randomly from a jar that contains 15 cards, numbered from 25 to 39. What is the probability that the card sel
VikaD [51]

Answer:

The probability that the card selected bears a number less than 34 is 0.3333.

Step-by-step explanation:

Let random variable <em>X</em> be defined as the number on the selected card.

There are <em>N</em> = 15 total cards.

The number on the cards are as follows:

S = {25, 26, 27,..., 38, 39}

The probability of an event, <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.

P(E)=\frac{n(E)}{N}

In this case we need to compute the probability that the card selected bears a number less than 34.

The favorable outcomes are:

<em>s</em> = {25, 36, 37, 38, 39}

<em>n</em> (X < 34) = 5

Compute the probability that the card selected bears a number less than 34 as follows:

P(X

                  =\frac{5}{15}\\\\=\frac{1}{3}\\\\=0.3333

Thus, the probability that the card selected bears a number less than 34 is 0.3333.

7 0
3 years ago
Other questions:
  • Draw a bar model that shows a pen is 4 times as long as an eraser that is 1 1/3 inches long.
    8·2 answers
  • What value of x makes the equation true ? 4(2x-4)=16
    6·2 answers
  • -5(1+7n)&gt;-38-2n<br><br> Solve
    11·1 answer
  • X 20) Becca has 3 times more games than Susan has. Write an algebraic
    6·1 answer
  • Determine if the table is proportional or nonproportional
    12·2 answers
  • 3(m - 4)² - 13 - (m² - 4)
    6·1 answer
  • Please help me with this question!!
    5·2 answers
  • Evaluate the expression 2(4-3) in two ways pls help
    13·1 answer
  • The sum of two numbers is 48.<br>the second number is seven times the first number​
    11·2 answers
  • Center: (10,-10)
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!