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4 years ago

14

How do I do this one

1 answer:

ira [324]4 years ago

8 0

think of x as one so you would graph y axis as 4 and x axis as 1

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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 .

<u>Puttting</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>1</u><u> </u><u>in</u><u> </u><u>f</u><u>(</u><u>x</u><u>)</u><u> </u><u>:</u><u>-</u>

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

$\rule{200}2$

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 .

<u>Putt</u><u>ting</u><u> </u><u>x</u><u> </u><u>=</u><u> </u><u>(</u><u>-</u><u>1</u><u>)</u><u> </u><u>:</u><u>-</u>

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

$\rule{200}2$

<u>Adding</u><u> </u><u>the</u><u> </u><u>above</u><u> </u><u>two</u><u> </u><u>equations</u><u> </u><u>:</u><u>-</u>

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

$\rule{200}2$

<u>Put</u><u> </u><u>this</u><u> </u><u>value</u><u> </u><u>of</u><u> </u><u>p</u><u> </u><u>in</u><u> </u><u>equation</u><u> </u><u>(</u><u>i</u><u>)</u><u> </u><u>.</u>

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

4 0

3 years ago

Taylor bought some jeans on sale. The number of jeans she bought is 1-fith the amount of money she spent. She bought 6 jeans. Fi

Rina8888 [55]

Answer:

30

Step-by-step explanation:

Let the amount of money Taylor spent = x

The number of jeans she bought is 1-fith the amount of money she spent. She bought 6 jeans.

Hence

1/5 × x = 6 jeans

x/5 = 6 jeans

Cross Multiply

x = 5 × 6 jeans

x = 30

The amount of money Taylor spent = 30

3 0

3 years ago

game stop is offering a sale on used Nintendo 360 games. They put together sale packs of 5 for $44.75. what is the unit price of

Arada [10]

Divide the total cost by the number of games.

44.75 ÷ 5 = 8.95

Each game costs $8.95.

8 0

4 years ago

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Jamal ran 8 kilometers, sprinted 500 meters, and climbed bleachers for a distance of 2 kilometers during track practice. How man

Margaret [11]

10,500 I think that would be the answer

5 0

4 years ago

A wrestling match has eliminations each round. The table below shows the number of wrestlers in each of the first 4 rounds of th

Mekhanik [1.2K]

<span>negative fifty five over three, on average, there were 55 fewer players for every 3 rounds

hope this helps</span>

6 0

3 years ago

Read 2 more answers