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d1i1m1o1n [39]
3 years ago
14

I need help understanding complex zeros of a polynomial function. I've taken notes, I've watched videos, nothing helps. I'm lost

and have been stuck on this for a week now.
Mathematics
1 answer:
allsm [11]3 years ago
4 0
Polynomials can have REAL ZEROS or COMPLEX ZEROS. Real Zeros to a polynomial are POINTS where the graph crosses the x-axis when y=0. When we graph each function, we can see these points. Complex Zeros are the SOLUTIONS of the equation that ARE NOT VISIBLE on the graph.
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Start time 11:00 am Elapsed time 4 hr and 5 min
vivado [14]
Well, if it starts on 11:00 am, add 4 hours = 3:00 + 5 min = end time = 3:05 am.
Hopes this helps ;)
8 0
3 years ago
Read 2 more answers
Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)
Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

\\AB = B - A =  (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k                 [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B =  (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k                 [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C =  (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k                [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D =  (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k                [Collect like terms]

DA = -i - 4j - 3k

AC = C - A =  (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k                [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k                [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD  [AB is parallel to CD]

AC = BD This implies that AC || BD  [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

<u>Now let's calculate the area</u>

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]

<u></u>

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = \sqrt{(-6)^2 + (-6)^2 + (10)^2}

|AB X AC| = \sqrt{172}

|AB X AC| = 13.15

Area = 13.15 square units.

<u></u>

<u></u>

<u>PS: </u> ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0
3 years ago
1 On a trip, a family drove 270 kilometers in 3 hours. a Find how many kilometers were traveled in one hour. Express this as a r
wolverine [178]
90 kilometers per hour
270/3=90
7 0
2 years ago
Read 2 more answers
Plot and label one point that is not a solution to the inequality shown in this graph.
AURORKA [14]

Answer:

any point on the graph that's not shaded

Step-by-step explanation:

you can just plot any point on the graph that's not shaded(because it's not a solution to the inequality).

for example, (3, -5) or (-4, -5) or (7, 0)

5 0
2 years ago
(2x^3+4x^2-3)+(6x^3+4x-4)<br>​
sukhopar [10]

Answer:

8x^3 + 4x^2 + 4x -7

Step-by-step explanation:

Add like terms.

8 0
3 years ago
Read 2 more answers
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