A polynomial functiion P(x) with rational coefficients has the given roots. find two additional roots of p(x)=0

1 answer:

8 0

If -2i is a root, then 2i is also a root. If √10 is a root, then -√10 is also a root. Convert all four of these roots into factors using the factor theorem (which says that if R is a root, then (x - R) is a factor). (x + 2i) (x - 2i) (x - √10) (x + √10) Multiply these factors together. (It's easiest to multiply the conjugate pairs together first.): x^4 - 6x^2 - 40

You might be interested in

A herd of 1,500 steer was fed a special high‐protein grain for a month. A random sample of 29 were weighed and had gained an ave

Marianna [84]

By formula we know that:

z (x) = (x - m) / [sd / sqrt (n)]

where x is the value we want to know (6.7), m is the mean (5), sd is the standard deviation (7.1) and n is the sample size (29).

Replacing we have:

z (6.7) = (6.7 - 5) / [7.1 / sqrt (29)]

z = 1.289

If we look in the normal distribution table (attached), we have that the probability is 0.8997, therefore:

1 - 0.8897 = 0.1003

So the conditional probability of a herd sample earning at least 6.7 pounds per steer is 10.03%.

Now the hypothesis tells me:

m> 5

The probability is somewhat low, therefore, the most correct thing is to reject the hypothesis even though it is a fact that can occur.

4 0

3 years ago

The base of a solid right pyramid is a regular hexagon with a radius of 2x units and an apothem of units. A solid right pyramid

Xelga [282]

Answer:

$6 x^2*\sqrt{3}$

Step-by-step explanation:

The base of the pyramid we need to study is a hexagon.

Let's look at the attached image of an hexagon to understand how we are going to find the area of this figure.

Notice that an hexagon is the combination of 6 exactly equal equilateral triangles in our case of size "2x" (notice that the "radius" of the hexagon is given as "2x")

Therefore the area of the hexagon is going to be 6 times the area of one of those equilateral triangles.

We know the area of a triangle is the product of its base times its height, divided by 2: $\frac{base*height}{2} = \frac{2x*height}{2}$

We notice that the triangle's height is exactly what is called the "apothem" of the hexagon (depicted in green in our figure) which measures $x\sqrt{3}$ , so replacing this value in the formula above for the area of one of the triangles: