All categories

3 years ago

Solve the equation x^4+7x^2-18=0 and express each solution in a+bi form

Mathematics

1 answer:

maw [93]3 years ago

4 0

Answer:

The following are the solutions found for x:

+√2 + 0i

-√2 + 0i

0 + 3i

0 - 3i

Step-by-step explanation:

The given equation is:

x⁴ + 7x² - 18 = 0

Rewrite x4 as (x²)²

(x²)² + 7x² − 18 = 0

Let u = x²

u² + 7u − 18 = 0

Factorize:

u² + 9u - 2u - 18 = 0

u(u+9) -2(u+9) = 0

(u-2)(u+9) = 0

(x²-2)(x²+9) = 0

Seperate both equations:

x² - 2 = 0 x² + 9 = 0

x = ±√2 x = ±√-9

x = ±√2 x = ± 3√-1

x = ±√2 + 0i x = 0 ± 3i

You might be interested in

When children are engaged in age appropriate actions that are annoying but not harmful, what should parents do?

alukav5142 [94]

C because do you not want your child participating age-apprioate activities if you think it is annoying you can leave that area

3 0

3 years ago

A watermelon seed is 0.4cm long. How far would a line of 126 stretch?

nikdorinn [45]

Answer:

0.504m

Step-by-step explanation:

First, we would multiply 0.4cm by 126 watermelon seeds to find the length of the line in cm.

0.4*126

= 50.4cm

Therefore, the line of watermelon seeds stretches 50.4cm.

Now, because the question wants us to type the answer in meters, we must convert 50.4cm into meters. We do this by dividing 50.4 by 100 since 100cm makes up 1 meter.

50.4/100

= 0.504m

Therefore, the line of watermelon seeds stretches 0.504m.

I hope this helps!

6 0

2 years ago

Simplify the following expression using only positive exponents. Help please!? It has to be only positive exponents the -9/7t an

wlad13 [49]

(-9t^25) / (7t^26) = -9 / (7t)

8 0

3 years ago

According to the National Vital Statistics, full-term babies' birth weights are Normally distributed with a mean of 7.5 pounds a

Sav [38]

Answer:

68.26% probability that a randomly selected full-term pregnancy baby's birth weight is between 6.4 and 8.6 pounds

Step-by-step explanation:

Problems of normally distributed samples are 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:

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

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.

In this problem, we have that:

$\mu = 7.5, \sigma = 1.1$