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3 years ago

Solve −3x2 − 4x − 4 = 0

Mathematics

2 answers:

Bond [772]3 years ago

7 0

The answer to the question is x= - 2 +or- 2i✓2 /3

Fynjy0 [20]3 years ago

6 0

Answer:

$x1=\frac{-2(+)2i\sqrt{2}} {3}$

$x2=\frac{-2(-)2i\sqrt{2}} {3}$

Step-by-step explanation:

we have

$-3x^{2} -4x-4=0$

Rewrite (Multiply by $-1$ both sides)

$3x^{2}+4x+4=0$

The formula to solve a quadratic equation of the form $ax^{2} +bx+c=0$ is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$3x^{2}+4x+4=0$

$a=3\\b=4\\c=4$

substitute

$x=\frac{-4(+/-)\sqrt{4^{2}-4(3)(4)}} {2(3)}$

$x=\frac{-4(+/-)\sqrt{-32}} {6}$

remember that

$i=\sqrt{-1}$

$x=\frac{-4(+/-)4i\sqrt{2}} {6}$

Simplify

$x=\frac{-2(+/-)2i\sqrt{2}} {3}$

$x1=\frac{-2(+)2i\sqrt{2}} {3}$

$x2=\frac{-2(-)2i\sqrt{2}} {3}$

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Can someone factor this problem for me?

Likurg_2 [28]

Your factored answer will be

(3x-4y) (x-5y)

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8 0

3 years ago

Read 2 more answers

A candidate for a US Representative seat from Indiana hires a polling firm to gauge her percentage of support among voters in he

UkoKoshka [18]

Answer:

a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

$(\sqrt{n})^2 = (\frac{1.96*0.5}{0.04})^2$

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$