Answer:
it must also have the root : - 6i
Step-by-step explanation:
If a polynomial is expressed with real coefficients (which must be the case if it is a function f(x) in the Real coordinate system), then if it has a complex root "a+bi", it must also have for root the conjugate of that complex root.
This is because in order to render a polynomial with Real coefficients, the binomial factor (x - (a+bi)) originated using the complex root would be able to eliminate the imaginary unit, only when multiplied by the binomial factor generated by its conjugate: (x - (a-bi)). This is shown below:
![(x-(a+bi))*(x-(a-bi))=\\(x-a-bi)*(x-a+bi)=\\([x-a]-bi)*([x-a]+bi)=\\(x-a)^2-(bi)^2=\\(x-a)^2-b^2(-1)=\\(x-a)^2+b^2](https://tex.z-dn.net/?f=%28x-%28a%2Bbi%29%29%2A%28x-%28a-bi%29%29%3D%5C%5C%28x-a-bi%29%2A%28x-a%2Bbi%29%3D%5C%5C%28%5Bx-a%5D-bi%29%2A%28%5Bx-a%5D%2Bbi%29%3D%5C%5C%28x-a%29%5E2-%28bi%29%5E2%3D%5C%5C%28x-a%29%5E2-b%5E2%28-1%29%3D%5C%5C%28x-a%29%5E2%2Bb%5E2)
where the imaginary unit has disappeared, making the expression real.
So in our case, a+bi is -6i (real part a=0, and imaginary part b=-6)
Then, the conjugate of this root would be: +6i, giving us the other complex root that also may be present in the real polynomial we are dealing with.
Answer:
x= 0
Step-by-step explanation:
Let's first simplify the equation to make the PEMDAS process easier.
8x-10=3x-10+7x
8x-10=10x-10
Now lets start the subtracting and dividing process.
8x=10x
0=2x
0=x
Answer:
The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups.
Step-by-step explanation:
A two sample t-test is used to compared the means of two samples who were exposed to different scenarios and therefore, it helps us to see the difference between these two samples.
In this problem, the teacher is experimenting with a new computer-based instruction. To be able to use the two-sample t-test she would have to have two randomly assigned samples and expose each of these two samples to different scenarios (one would receive a traditional instruction and the other one would receive a computer instruction), and finally she would need to compare the scores in both samples.
Therefore, the correct answer would be b) The teacher randomly divides the class into two groups. One of the groups receives computer-based instruction and the other group receives traditional instruction without computers. After instruction, each student takes a test and the teacher wants to compare the test scores of the two groups.
<u>*Option A is incorrect</u> because the students are only exposed to the lesson using a computer program and therefore they aren't exposed to different scenarios.
<u>*Option C is incorrect</u> because although in this case the teacher uses both traditional and computer methods, there are not two different samples and she only gets the opinion of the students which is not an exact method of getting information on the effectiveness of the computer based method.
Answer:
-6 -7 -8 -9 -10
Step-by-step explanation:
anything that keeps going from there dont do anything like -5 -4 -3 -2 -1 because it would be wrong
any negative number that keeps increasing after -6
Answer:
2 min.
Step-by-step explanation:
1h is 60 min so divide 60 by 30 and you get 2
