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Travka [436]
3 years ago
6

Can a quadratic have one real and one non real root

Mathematics
1 answer:
alukav5142 [94]3 years ago
3 0

Answer:

Yes, it is possible. We already know that complex roots exist in conjugate pair but the case is true only when the equation has real coefficients. But on the other hand, if the equation has complex coefficients, then it is possible to attain one real and one complex root.

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For what values of <img src="https://tex.z-dn.net/?f=x" id="TexFormula1" title="x" alt="x" align="absmiddle" class="latex-formul
11Alexandr11 [23.1K]

Answer:

x1

Step-by-step explanation:

We have:

(x+5)(x-1)

And we want to find the value of x such that the expression is positive. So, we can write this as the following inequality:

(x+5)(x-1)>0

Solve for the inequality. First, we can solve for the zeros like a normal quadratic. So, pretend the inequality is with an equal sign:

(x+5)(x-1)=0

Zero Product Property:

x+5=0\text{ or } x-1=0

On the left, subtract 5.

On the right, add 1.

So, our zeros are:

x=-5, 1

Since our inequality is a <em>greater than</em>, our answer is an "or" inequality with our answer being all the values to the <em>left</em> of our lesser zero and all the values to the <em>right </em>of our greater zero.

So, our solution is:

x1

And we're done!

7 0
3 years ago
Read 2 more answers
At a large Midwestern university, a simple random sample of 100 entering freshmen in 1993 found that 20 of the sampled freshmen
guajiro [1.7K]

Answer:

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

p1 -> 1993

20 out of 100, so:

p_1 = \frac{20}{100} = 0.2

s_1 = \sqrt{\frac{0.2*0.8}{100}} = 0.04

p2 -> 1997

10 out of 100, so:

p_2 = \frac{10}{100} = 0.1

s_2 = \sqrt{\frac{0.1*0.9}{100}} = 0.03

Distribution of p1 – p2:

p = p_1 - p_2 = 0.2 - 0.1 = 0.1

s = \sqrt{s_1^2+s_2^2} = \sqrt{0.04^2 + 0.03^2} = 0.05

Confidence interval:

p \pm zs

In which

z is the z-score that has a p-value of 1 - \frac{\alpha}{2}.

90% confidence level

So \alpha = 0.1, z is the value of Z that has a p-value of 1 - \frac{0.1}{2} = 0.95, so Z = 1.645.  

The lower bound of the interval is:

p - zs = 0.1 - 1.645*0.05 = 0.01775&#10;

The upper bound of the interval is:

p + zs = 0.1 + 1.645*0.05 = 0.18225&#10;

The 90% confidence interval for the difference of proportions is (0.01775,0.18225).

6 0
3 years ago
Please help Use the expression 8a + 16c.
alexdok [17]

Answer:

C  89a + 2c)

Step-by-step explanation:

The largest factor of both 8 and 16 is 8.  So, 8 = GCF

factor out an 8 and you get 8(a + 2c)

To check if you are correct, multiply and see if you get what you started with.

3 0
3 years ago
Read 2 more answers
Help meee plssssssssssssssssssssssssssss
Drupady [299]

Answer:

either a or c no problem nskskdjdjd

3 0
3 years ago
The line segment formed by joining points A (-1,y) B (0,0), and the line segment joined by forming points C (6,3) D (8,9) share
Airida [17]

Answer:

<h3>-3</h3>

Step-by-step explanation:

For two parallel lines. their slope are equal

Find the slope of each of the lines

For line A;

m = 0 -y/0+1

mA = -y/1

For line B;

mB = 9 - 3/8 - 6

mB = 6/2

mB = 3

since their slope are equal hence mA = mB

-y/1 = 3

-y = 3

y = -3

Hence the value of y is -3

8 0
3 years ago
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