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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.
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Sveta_85 [38]

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3 years ago
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3 years ago
The quotient of 8 times a number and the cube root of the number
galben [10]

Answer:

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Step-by-step explanation:

n/8...

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3 0
3 years ago
Can I have help with the question
sleet_krkn [62]

Answer:

Midpoint = (3.5, 4.5)

Perpendicular bisector = y =  \frac{7}{9} x + \frac{16}{9}

Step-by-step explanation:

[] We can solve this using the midpoint formula:

-> See attached

[] Plug-in our coordinates and solve:

(\frac{7+0}{2} ,\frac{0+9}{2} )=(\frac{7}{2} ,\frac{9}{2} )=(3.5,4.5 )

[] Now we will find the slope to solve for the perpendicular bisector.

-> We will use slope-intercept form, see attached

\frac{9-0}{0-7}=\frac{9}{-7}

-> The slopes of two perpendicular lines are negative reciprocals of each other, so \frac{7}{9} will be the slope of or perpendicular bisector

-> Now we can solve for the equation by using y – y1 = m ( x – x1), were y1 and x1 are the coordinates of our midpoint

y - 4.5 = \frac{7}{9} (x-3.5)

y - 4.5 = \frac{7}{9} x-\frac{49}{18}

y = \frac{7}{9} x-\frac{49}{18} + 4.5

y =  \frac{7}{9} x + \frac{16}{9}

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

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2 years ago
The ratio of the measures of the angles in cat is 2:7:9. find the measure of the smallest angle.
iren2701 [21]

Answer:

20º

Step-by-step explanation:

Total parts

2  + 7 + 9 = 18

Value of each part given 180º in a triangle

180 / 18 = 10º

Smallest angle

2 * 10 = 20º

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2 years ago
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