Rational Expressions and Functions Unit Test Need answers please
1 answer:
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Answer: The answer is given below.
Step-by-step explanation: The given circles are:
Circle 1: centre (2, 3) and radius 4
Circle 2: centre (2, 3) and radius 12.
The equations of circle 1 and circle 2 are respectively given as :
These two circles are drawn on the graph as shown in the attached figure.
We can easily see that the Circle 2 is a dilation of Circle 1 with a scale factor
Thus, the two circles are similar.
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:
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.