First, you need to get delta which is b squared minus 4ac. If delta is higher than cero, the polynomial has two solutions, if it is less, the polynomial has no real solutions and if it is the same, it has one solution.Although that is only for second grade ecuations

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One can determine the number of roots by seeing the degree of the given polynomial.

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Step-by-step explanation:

The number of roots can be determine by just seeing the highest power of the given equation.

Example,

1) for the equation

*

here, the highest power the equation is one. So, it will have one root.

Lets check it by simplify

*

Hence, the equation has only one root namely x = 4.

2) Consider a quadratic equation,

*

here, the highest power the equation is two.So, it will have two roots.

Lets check it by simplify using middle term splitting method,

*

*

*

*
or
*

thus, the equation has two roots.

Hence, one can determine the number of roots by seeing the degree of the given polynomial.


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96.08% probability that their mean rebuild time is less than 8.9 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean

*
and standard deviation
*
, the zscore of a measure X is given by:

*

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean

*
and standard deviation
*
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
*
and standard deviation
*
.

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For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.