Answer:
a) ![P (x) = (x + 3) (x-1) (x-4)](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%28x%20%2B%203%29%20%28x-1%29%20%28x-4%29)
b) ![P (x) = (2x + 5) (5x - 4) (x-6)](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%282x%20%2B%205%29%20%285x%20-%204%29%20%28x-6%29)
c) ![P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%28x-3%29%20%28x-1%29%20%28x-4%29%20%28x%20%2B%201%29%20%5E%202)
Step-by-step explanation:
<u>For the question a *</u> you need to find a polynomial of degree 3 with zeros in -3, 1 and 4.
This means that the polynomial P(x) must be zero when x = -3, x = 1 and x = 4.
Then write the polynomial in factored form.
![P (x) = (x + 3) (x-1) (x-4)](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%28x%20%2B%203%29%20%28x-1%29%20%28x-4%29)
Note that this polynomial has degree 3 and is zero at x = -3, x = 1 and x = 4.
<u>For question b, do the same procedure</u>.
Degree: 3
Zeros: -5/2, 4/5, 6.
The factors are
![x = -\frac{5}{2}\\\\x +\frac{5}{2} = 0\\\\(2x +5) = 0](https://tex.z-dn.net/?f=x%20%3D%20-%5Cfrac%7B5%7D%7B2%7D%5C%5C%5C%5Cx%20%2B%5Cfrac%7B5%7D%7B2%7D%20%3D%200%5C%5C%5C%5C%282x%20%2B5%29%20%3D%200)
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![x =\frac{4}{5}\\\\x-\frac{4}{5} = 0\\\\(5x-4) = 0](https://tex.z-dn.net/?f=x%20%3D%5Cfrac%7B4%7D%7B5%7D%5C%5C%5C%5Cx-%5Cfrac%7B4%7D%7B5%7D%20%3D%200%5C%5C%5C%5C%285x-4%29%20%3D%200)
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![x = 6\\\\(x-6) = 0](https://tex.z-dn.net/?f=x%20%3D%206%5C%5C%5C%5C%28x-6%29%20%3D%200)
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![P (x) = (2x + 5) (5x - 4) (x-6)](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%282x%20%2B%205%29%20%285x%20-%204%29%20%28x-6%29)
<u>Finally for the question c we have</u>
Degree: 5
Zeros: -3, 1, 4, -1
Multiplicity 2 in -1
![x = -3\\\\(x-3) = 0](https://tex.z-dn.net/?f=x%20%3D%20-3%5C%5C%5C%5C%28x-3%29%20%3D%200)
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![x = 1\\\\(x-1) = 0](https://tex.z-dn.net/?f=x%20%3D%201%5C%5C%5C%5C%28x-1%29%20%3D%200)
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![x = 4\\\\(x-4) = 0](https://tex.z-dn.net/?f=x%20%3D%204%5C%5C%5C%5C%28x-4%29%20%3D%200)
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![x = -1\\\\(x + 1) = 0](https://tex.z-dn.net/?f=x%20%3D%20-1%5C%5C%5C%5C%28x%20%2B%201%29%20%3D%200)
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![P (x) = (x-3) (x-1) (x-4) (x + 1) ^ 2](https://tex.z-dn.net/?f=P%20%28x%29%20%3D%20%28x-3%29%20%28x-1%29%20%28x-4%29%20%28x%20%2B%201%29%20%5E%202)
Answer:
7 -5i
Step-by-step explanation:
The additive inverse is the number we add to make it equal to zero
-7+5i + x = 0
the real part
-7 + x = 0
x = 7
The imaginary part
5i+x = 0
x = -5i
The complex x is
7 -5i
Notice it is the opposite of the number
- (-7+5i)
7-5i
A). because B,C, and D didnt really make any sence
Answer:
The distance from his starting point is <u>6.7 m</u>.
Step-by-step explanation:
Given:
Shane marched 3 m East and 6 m north.
Now, to get the distance from his starting point.
Let the distance from the starting point be ![x.](https://tex.z-dn.net/?f=x.)
Now, to solve using pythagorean theorem:
![AB^2+BC^2=AC^2](https://tex.z-dn.net/?f=AB%5E2%2BBC%5E2%3DAC%5E2)
![6^2+3^2=x^2](https://tex.z-dn.net/?f=6%5E2%2B3%5E2%3Dx%5E2)
![36+9=x^2](https://tex.z-dn.net/?f=36%2B9%3Dx%5E2)
![45=x^2](https://tex.z-dn.net/?f=45%3Dx%5E2)
<em>Using square root on both sides we get:</em>
![6.71=x\\\\x=6.71\ m.](https://tex.z-dn.net/?f=6.71%3Dx%5C%5C%5C%5Cx%3D6.71%5C%20m.)
<u>So, the distance from the starting point nearest to tenth is 6.7 m.</u>
Therefore, he is 6.7 m from his starting point.