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Nostrana [21]
3 years ago
11

Describe three different ways to solve a quadratic equation. Describe the strengths and limitations of each method, and explain

how you would decide which one to use to solve a particular problem.
Mathematics
2 answers:
katen-ka-za [31]3 years ago
7 0
There are 3 different ways to solve a quadratic.

Method one

The quadratic can be graphed. This is very useful to lead in the direction of a solution. Some graphing programs give you a very good hint at what your answer is going to be. Sometimes not. A graph is most useful when you are dealing with a problem like 
y = 3x + 2
y = x^2 - 5x + 6 where you want to know where the x and y values are the same for both equations. It may not give you an accurate answer, but it will tell you if the answers you got using other methods is correct.

It you need accurate answers and the the graph is not giving you good points then a graph is not that helpful.

Method Two
You could use the quadratic formula. It will give you an accurate answer but only if you don't make a mistake in the arithmetic. That's not a trivial consideration. If you are dealing with numbers like 3.444x^2 - 88.77x - 44.99 = 0 you have 2 major problems. One is not making a mistake and the other is knowing when to round. But in general, this is a fail safe method.

Method Three
You could try factoring. If it works, it's by far the quickest and in it's own way the most accurate. It is not always easy to see how numbers may factor. For instance, this quadratic can be factored, but is it worth finding out how?
y = 144x^2 + 560x - 221

Completing the Square
There are other methods that can be used. Completing the square is one of them. That gives the vertex which can also give the roots. It is prone to errors as well. If handled carefully, it is a good way to solve a quadratic. 
y = (x - 2)^2 - 4 will give you the vertex immediately and the roots if y is made to be 0. It will give you he y intercept by making x = 0 Those are the 5 major points of a quadratic is this is pretty useful. It's disadvantage is that people find it cumbersome to arrive at.

One Last Way
Lastly if all else fails, you could look for a program on the internet.
almond37 [142]3 years ago
3 0

Answer:

The three ways to solve a quadratic equation are the quadratic formula, factoring, and square roots. The quadratic formula can be used to solve for x, factoring can help you find the numbers that lead you to the root numbers. Square roots can help you also find the roots of the question. The limitation of the quadratic formula is that it you may not get a whole number. Factoring can be only most useful on graphs. The limitation of square roots is that it is long.

Step-by-step explanation:

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An area of 4 square yards is equal to 36 square feet. 10 square yards is equal to how many square feet?
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Read 2 more answers
For the given hypothesis test, determine the probability of a Type II error or the power, as specified. A hypothesis test is to
erica [24]

Answer:

the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251

Option A) is the correct answer.

Step-by-step explanation:

Given the data in the question;

we know that a type 11 error occur when a null hypothesis is false and we fail to reject it.

as in it in the question;

obtained mean is 9.8 which is obviously not equal to 8.3

But still we fail to reject the null hypothesis says mean is 8.3

Hence we have to find the probability of type 11 error

given that; it is right tailed and o.5, it corresponds to 1.645

so

z is equal to 1.645

z = (x-μ)/\frac{S}{\sqrt{n} }

where our standard deviation s = 3.8

sample size n = 50

mean μ = 8.3

we substitute

1.645 = (x - 8.3)/\frac{3.8}{\sqrt{50} }

1.645 = (x - 8.3) / 0.5374

0.884023 = x - 8.3

x = 0.884023 + 8.3

x = 9.18402

so, by general rule we will fail to reject the null hypothesis when we will get the z value less than 1.645

As we reject the null hypothesis for right tailed test when the obtained test statistics is greater than the critical value

so, we will fail to reject the null hypothesis as long as we get the sample mean less than 9.18402

Now, for mean 9.8 and standard deviation 3.8 and sample size 50

Z =  (9.18402 - 9.8)/\frac{3.8}{\sqrt{50} }

Z = -0.61598 / 0.5374

Z = - 1.1462 ≈ - 1.15

from the z-score table;

P(z<-1.15) = 0.1251

Therefore, the probability of a Type II error if in fact the mean waiting time u, is 9.8 minutes is 0.1251

Option A) is the correct answer.

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