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:
Base = 10 cm
Height = 60 cm
Step-by-step explanation:
The formula for the area of a triangle is 
, where <em>b</em> is the length of the base of the triangle, and <em>h</em> is the length of the height of the triangle.
We know the area is 300, and since the height of the triangle is 6 times its base, we know that 
. We can plug in these values into our formula for the area of a triangle, which gives us the following equation to solve:
The base of the triangle is 10 centimeters.
Now that we know the base of the triangle, we can plug its value in to the original formula to solve for the height of the triangle, which gives us the following equation:
The height of the triangle is 60 centimeters.
Given A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 8, 10}, C = {1, 5, 6, 7, 9}
andrey2020 [161]
Answer:
ummmm thats not even a question
Step-by-step explanation:
Answer:
The line would be y = 2x + 5
Step-by-step explanation:
To find a parallel line, we first need to note that the slope of the original line is 2. This means the slope of our new line will also be 2 because parallel lines have the same slope.
So we use the slope we found along with the point given in point-slope form. Then we solve for y.
y - y1 = m(x - x1)
y - 11 = 2(x - 3)
y - 11 = 2x - 6
y = 2x + 5
Answer:
Just add the two answers together I think
Step-by-step explanation:
300 + 5 = 305
