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Hunter-Best [27]
4 years ago
14

If a polynomial function f(x) has roots -8, 1, and 6i, what must also be a root of f(x)?

Mathematics
1 answer:
Naddik [55]4 years ago
5 0

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

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.

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3/4 and 15/20

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3 years ago
Diagram shows an irregular hexagon PQRSTU.Fine the value of X + Y=
Lynna [10]
To find the value of x+y, we will first find the sum of all the interior angles of the hexagon.The sum of the interior angles in a hexagon is always equal to 720 degrees.

All the angles in the diagram are in terms of x or y except for angle t. However, we know that the corresponding exterior angle is 30 degrees. The sum of angle t and 30 is 360. We can solve this in an algebraic equation.

t+30=360
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Now, we can solve for the values of x+y. We can set this up in another algebraic equation.

x+x+x+2y+y+30=720

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6 0
4 years ago
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nekit [7.7K]
<span>0.5 +x(0.5)
Hope this helped!</span>
7 0
4 years ago
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HELP ANSWER BOTH PLEASE (╥﹏╥)​
pogonyaev

Answer:

a.) 61 square feet

b.) $152.50

Step-by-step explanation:

first you find the area for the rectangle

LxW=A

10x4=40

then you find the area for the triangle

(bxh)1/2=a

(6x7)1/2=21

-we get 7 from adding the height that we know (3ft) and using logic, a rectangle has equal parallel lines so the dotted line has to equal 4ft. so 3ft+4ft=7ft

then you add both areas together

40 square feet+21 square feet= 61 square feet

<em>Now</em><em> </em><em>for</em><em> </em><em>B</em><em>.</em><em>)</em>

as we know, the area of the room floor is 61sq feet. so by multiplying 2.5 and 61 you get the cost as $152.50

8 0
4 years ago
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