Can you guys answer this please

5. f(x) = x ^ 3 + p * x ^ 2 + qx + 6 (a) Find the value of each constants p and q, given that (x - 1) is a factor of f(x) and wh

lara31 [8.8K]

Answer:

$\boxed{\textsf{ The value of p is \textbf{-2} and the value of q is \textbf{ -5}.}}$

Step-by-step explanation:

A polynomial is given to us and we need to find the value of the constants in the given equation . The given polynomial to us is :-

$\sf\implies f(x)= x^3+px^2+qx + 6$

It's mentioned that (x - 1) is a factor of f(x) . This means on putting x = 1 in the given polynomial the value of the polynomial becomes 0 .

Puttting x = 1 in f(x) :-

$\sf\implies f(x)= x^3+px^2+qx + 6 \\\\\sf\implies f(1) = 1^3 + p(1)^2+q(1) + 6 = 0 \\\\\sf\implies f(1)= 1+p + q + 6 = 0 \\\\\sf\implies \boxed{ \red{\sf p + q = -7 }}$

$\rule{200}2$

Now secondly it's given that on dividing the given polynomial by (x + 1) , the remainder is 8 . This means that on putting x = -1 the value of the given polynomial becomes 8 .

Puttting x = (-1) :-

$\sf\implies f(x)= x^3+px^2+qx + 6 \\\\\sf\implies f(-1) = (-1)^3 + p(-1)^2+q(-1)+6 = 8 \\\\\sf\implies f(-1)= -1+p -q + 6 = 8 \\\\\sf\implies p - q = 8 -6 +1 \\\\\sf\implies \boxed{ \red{\sf p - q = 3 }}$

$\rule{200}2$

Adding the above two equations :-

$\sf\implies p + q + p - q = -7 + 3 \\\\\sf\implies 2p = -4 \\\\\sf\implies p =\dfrac{-4}{2}\\\\\sf\implies \boxed{\pink{\frak{ p = (-2) }}}$

$\rule{200}2$

Put this value of p in equation (i) .

$\sf\implies p + q = -7 \\\\\sf\implies -2 + q = -7 \\\\\sf\implies q = -7+2 \\\\\sf\implies \boxed{\pink{\frak{ q = (-5) }}}$

4 0

3 years ago

It is possible for a computer to pick up an erroneous signal that does not show up as an error on the screen. The error is calle

son4ous [18]

Answer:

Step-by-step explanation:

Using the concept of binomial probability distribution to approach the question.

Mathematically; P(X=r) = nCr P^r (1-p)^n-r

The steps is as shown in the attached file.

8 0

4 years ago

The table shows ticket prices at the movie 16 theater.Let a represent the number of adult tickets, c the number of childrens tic

enyata [817]

A. write an expression for the total cost of the three types of tickets. 
adults cost:$8.75
childrens cost:$6.50
senior citizen cost:$6.50 
so from the given data, the expression for the total cost at the movie 16 theater total cost = 8.75a + 6.50a + 6.50s

5 0

3 years ago

Antonio orders an iPhone case off of Amazon for $27. He has to pay an additional 3% for shipping and handling. How much will his

Wewaii [24]

Answer:

We conclude that total cost/bill will be: $27.81

Step-by-step explanation:

Given

The cost of an iPhone case = $27

Additional expense = 3% = 3/100 = 0.03

To determine

Total bill = ?

The expense amount can be calculated by multiplying the cost of an iPhone case by the additional expense

i.e.

Expense Amount = cost of an iPhone case × additional expense

= 27 × 0.03

= $0.81

The total cost is calculated by adding the expense amount and the original cost of an iPhone case.

i.e.

Total cost/bill = Expense Amount + cost of an iPhone case

= $0.81 + $27

= $27.81

Therefore, we conclude that total cost/bill will be: $27.81

6 0

3 years ago

Please help me with this

Free_Kalibri [48]

Answer:

$62.50

Step-by-step explanation: 250 divided by 4 equals $62.10

6 0

3 years ago