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3 years ago

The roots of x^2-()+34 are 5+3i

Mathematics

2 answers:

krek1111 [17]3 years ago

5 0

Answer:

We're given the roots of a quadratic function.

And, we are looking for the middle term.

Since the Quadratic Formula is used to determine the roots of a quadratic function, we can use the Quadratic Formula to get the value of the coefficient of the middle term.

ax² + bx + c ← Standard form ... Notice that there are two plus signs

x² − (__) + 34 ← This is what we're given

x² − mx + 34 ← This is what we know ... Now, put this in standard form

➊ x² + (-m)x + 34 ← a = 1, b = -m, c = 34

-b ± √(b²-4ac)

x = ——————— ← Rewrite this as two fractions to fit the form of 5±3i

-b √(b²-4ac)

x = —— ± ————— ← Compare this to 5 ± 3i

2a 2a

So,

-b -(-m)

——– = ——–– = 5 ⇒ m = 10a ⇒ m = 10

2a 2a

Therefore,

➊ x² + (-m)x + 34

x² − mx + 34 ← Now, substitute 10 for m

x² − 10x + 34 ← ANSWER

Step-by-step explanation:

wolverine [178]3 years ago

5 0

Answer:

try socratic it helps also

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Read 2 more answers

A small town has 2000 families. The average number of children per family is mu = 2.5, with a standard deviation sigma = 1.7. A

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Answer:

Let X the random variable that represent the number of children per fammili of a population, and for this case we know the following info:

Where $\mu=2.5$ and $\sigma=1.7$

We select a sample of n =64 >30 and we can apply the central limit theorem. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And for this case the standard error would be:

$\sigma_{\bar X} = \frac{1.7}{\sqrt{64}}= 0.2125$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

Let X the random variable that represent the number of children per fammili of a population, and for this case we know the following info:

Where $\mu=2.5$ and $\sigma=1.7$

We select a sample of n =64 >30 and we can apply the central limit theorem. From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})$

And for this case the standard error would be:

$\sigma_{\bar X} = \frac{1.7}{\sqrt{64}}= 0.2125$

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