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yarga [219]
3 years ago
13

Is there a way to simplify the process of plugging in factors through synthetic division to find the zeros of a polynomial? I am

aware of Descarte's Rule of Signs, but is there any other way to make it faster than guess-and-check?
Mathematics
1 answer:
Iteru [2.4K]3 years ago
4 0
Yes you can use the discriminant of a quadratic/polynomial. For instance, if
b^2 - 4ac = 0 there is one real root. If b^2 - 4ac > 0 there are two real roots and ib^2 - 4ac < 0  there are no real roots

The discriminant comes from the quadratic equation, which is the following.
x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}
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What is the solution to this equation?<br> 3x- x+8+5x-2=10
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3 years ago
The line width used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a st
Alinara [238K]

Answer:

There is a 0.82% probability that a line width is greater than 0.62 micrometer.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by

Z = \frac{X - \mu}{\sigma}

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. The sum of the probabilities is decimal 1. So 1-pvalue is the probability that the value of the measure is larger than X.

In this problem

The line width used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5 micrometer and a standard deviation of 0.05 micrometer, so \mu = 0.5, \sigma = 0.05.

What is the probability that a line width is greater than 0.62 micrometer?

That is P(X > 0.62)

So

Z = \frac{X - \mu}{\sigma}

Z = \frac{0.62 - 0.5}{0.05}

Z = 2.4

Z = 2.4 has a pvalue of 0.99180.

This means that P(X \leq 0.62) = 0.99180.

We also have that

P(X \leq 0.62) + P(X > 0.62) = 1

P(X > 0.62) = 1 - 0.99180 = 0.0082

There is a 0.82% probability that a line width is greater than 0.62 micrometer.

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Step-by-step explanation:

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