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: the correct answer is 9(x2+6x+9)=103 so it’s d
Step-by-step explanation:
Did it on edgunity
Answer:
see below
Step-by-step explanation:
The graph opens upward if the sign of the squared term is positive. If that sign is negative, the graph opens downward. The first three equations open upward; the last opens downward.
The line of symmetry is the value of x that makes the squared term zero. Here, that is x=5 for all equations.
<u>y=2/3(x-5)^2</u>: A, D
<u>y=1/2(x-5)^2</u>: A, D
<u>y=3/4(x-5)^2</u>: A, D
<u>y=-4(x-5)^2</u>: B, D
That is false
If x=8 then the whole thing is 24+6 which is 30
so 30<25 is false
Answer:
x = -5
y = 6
Step-by-step explanation:
3x + 7y = 27 --------------(I)
-3x + y = 21 -----------(II)
Add equation (I) & (II) and so x will be eliminated and we can find the value of y.
(I) 3x + 7y = 27
(II) <u> -3x + y = 21 </u> {add}
8y = 48
y = 48/8
y = 6
Plugin y = 6 in equation (I)
3x +7*6 = 27
3x + 42 = 27
3x = 27 - 42
3x = -15
x = -15/3
x = -5
