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:
1 3/4
Step-by-step explanation:
You can set it up like the distrubtive property first
3/4(2+ 1/3) Next you use the distirbutive property instead of adding inside the parenthesis and you multiply the 3/4 by 2 and then the 3/4 by 1/3
Use 2 as 2/1 in fraction problems
3/4 * 2/1 Now multiply the numerators together and the denomenators together
3 * 2 = 6 4 * 1 =4
6/4
3/4 *1/3
3 * 1 =3
4 * 3 =12
3/12
Now we have to make them both like terms (same denominator) so we can add them, we will multiply the 6/4 by 3 (Both top and bottom)
6 * 3 = 18 4 *3 =12
18/12
Now we add the fractions
3/12 +18/12 = 21/12
Reduce that and you get
21/12 = 1 9/12 or 1 3/4
Answer:
I think the answer is (3,10) sorry if I got this wrong!
Step-by-step explanation:
Answer:
y=negative 2x+1
Step-by-step explanation:
rise over run negative 14 over 7 equals negative 2 and the y intercept is 1
Answer:
$48.69
Step-by-step explanation:
45.50 + (45.50 * 0.07) = 48.69
hope this helps!
