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SVEN [57.7K]
3 years ago
10

Solve for x: x5 + x4 − 7x3 − 7x2 − 144x − 144 = 0

Mathematics
2 answers:
motikmotik3 years ago
6 0

x^5 + x^4 - 7x^3 - 7x^2 -144x - 144 = 0 \\x^4(x+1)-7x^2(x+1)-144(x+1)=0\\(x^4-7x^2-144)(x+1)=0\\\\x+1=0\Rightarrow x=-1\\\\x^4-7x^2-144=0\\x^4-16x^2+9x^2-144=0\\x^2(x^2-16)+9(x^2-16)=0\\(x^2+9)(x^2-16)=0\\(x^2+9)(x-4)(x+4)=0\\\\x^2+9=0\vee x-4=0 \vee x+4=0\\x=4 \vee x=-4\\\\x\in\{-4,-1,4\}

Zanzabum3 years ago
5 0

Answer:

{ -1, -3i,3i,4,-4}

Step-by-step explanation:

I'm going to try to get the Rational Root Theorem to work for us.

Since the coefficient of leading term is 1 we just need to look at the factors of the constant.

Possible rational zeros are going to be the factors of -144.

So here are some possible rational zeros: 1,2,3,4,6,8,9,12,16,18,24,36,48,72 and also the negative version of these numbers are numbers we must consider.

I'm going to see if -1 works.  

(-1)^5+(-1)^4-7(-1)^3-7(-1)^2-144(-1)-144

-1   +   1     +7      -7       +144  -144=0

So -1 is a zero so x+1 is a factor. I'm going to use synthetic division to see what multiplies to x+1 that will me the initial polynomial expression we had.

-1   |    1       1      -7        -7      -144    -144

     |           -1      0          7        0       144

     | ________ __________________

          1      0     -7         0       -144      0

So the (x+1)(x^4-7x^2-144)=0

The cool thing is that other factor is a sort of quadratic in disguise. That is it becomes a quadratic if you let u=x^2. So let's do that.

u^2-7u-144=0

(u+9)(u-16)=0

u=-9 or u=16

So x^2=-9 or x^2=16.

Square rooting both sides gives us:

x= \pm 3i \text{ or } x=\pm 4

So the solution set is { -1, -3i,3i,4,-4}

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Mice21 [21]

Answer:

y= -2/1x -4

Step-by-step explanation:

Hope it helped!

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2 years ago
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9 - 10x = 2x + 1 - 8x
Furkat [3]

Answer:

x=2

Step-by-step explanation:

9 - 10x = 2x + 1 - 8x

9-10x=-6x+1

Subtract 9 from both sides:

9-10x-9=-6x+1-9

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Add 6x to both sides:

-10x+6x=-6x-8+6x

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Divide both sides by -4:

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3 years ago
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tino4ka555 [31]

Answer:

  • 0.0000008

Step-by-step explanation:

<u>Given</u>

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3 years ago
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Given the quadratic function f(x) = 2x + 5x-12, what is the value of f(-2)?
tino4ka555 [31]

Answer:

-26

Step-by-step explanation:

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3 years ago
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Through: (-5, -5), slope=2/5
kakasveta [241]

For this case we have that by definition, the equation of a line in the slope-intersection form is:

y = mx + b

Where:

m: It is the slope

b: It is the cut point with the y axis

The slope is: m = \frac {2} {5}

Thus, the equation is of the form:

y = \frac {2} {5} x + b

We substitute the given point and find "b":

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3 years ago
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