All categories

2 years ago

1. If x³ +3x²-4=0 has x=-2 as a root (zero), find the other two roots.

Mathematics

1 answer:

castortr0y [4]2 years ago

6 0

Answer:

1 and -2 (has a multiplicity of 2)

Step-by-step explanation:

so since x=-2 is a root then (x+2) is a factor of the polynomial. This means you can divide the polynomial by (x+2) by using synthetic or long division. So for this example I'll using synthetic division which is much more simple than long division

-2 | 1 3 0 -4

-2 -2 4

1 1 -2 0

(x+2)(x²+x-2)

Now you can factor the quadratic into

(x+2)(x-1)

x+2 = 0

x = - 2

x-1 =0

x = 1

You might be interested in

20$ - 5$ = 15$ 15$/2.50 = 6 in graph form

max2010maxim [7]

Errorgccfcrcghutfcrvgvtvfvtby

4 0

3 years ago

The sum of two numbers is 4560892,if one of them 283651,find the other.

fomenos

Answer:

The answer is 4,277,241

Step-by-step explanation:

I subtracted 283,651 from 4560892.

7 0

3 years ago

Read 2 more answers

A quiz consists of 10 multiple choice questions, each with five possible answers, one of which is correct. to pass the quiz a

blsea [12.9K]

The probability is 0.006, or 0.6%.

This is binomial; there are a fixed number of trials (10), the events are independent (the chances of one occurring do not affect the chances of the other occurring), and there are two outcomes (either right or wrong).

He must get 6 of the 10 questions correct, so k is 6 and n is 10. The probability of getting a question correct is 1/5=0.2; the probability of getting a question incorrect is 4/5=0.8.

$_{10}C_6\times(0.2)^6\times(1-0.2)^{10-6}
\\
\\\frac{10!}{6!4!}\times(0.2)^6\times(0.8)^4
\\
\\210(0.2)^6\times(0.8)^4=0.0055\approx0.006$

6 0

4 years ago

please help :( I know that <img src="https://tex.z-dn.net/?f=2%5E%5Cfrac%7B6%7D%7B5%7D" id="TexFormula1" title="2^\frac{6}{5}" a

saul85 [17]

Answer:

$\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}$

Step-by-step explanation:

Fractional Exponents

An expression like

$\displaystyle a^{\frac{n}{m}}$

can be expressed as a radical of the form:

$\sqrt[m]{a^n}$

We have the expression:

$\displaystyle 2^{\frac{6}{5}}$

Its equivalent radical form is:

$\displaystyle 2^{\frac{6}{5}}=\sqrt[5]{2^6}$

Since the exponent is greater than the index of the radical, we can take 2 out of it by following the procedure:

$\sqrt[5]{2^6}=\sqrt[5]{2^5\cdot 2}$

Taking out $2^5$ from the radical:

$\sqrt[5]{2^6}=2\sqrt[5]{2}$

Thus:

$\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}$

4 0

3 years ago

How do you find a volume of a cone?

Dennis_Churaev [7]

Answer:

V = (1/3)πr²h

Step-by-step explanation:

The volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

Cylinder Volume = πr²h

Cone Volume = (1/3)πr²h

where r is the radius (of the base), and h is the height perpendicular to the circular base.

_____

Comment on area and volume in general

You will note the presence of the factor πr² in these formulas. This is the area of the circular base of the object. That is, the volume is the product of the area of the base and the height. In general terms, ...

V = Bh . . . . . for an object with congruent parallel "bases"

V = (1/3)Bh . . . . . for a pointed object with base area B.

This is the case for any cylinder or prism, even if the parallel bases are not aligned with each other. (That is, it works for oblique prisms, too.)

Note that the cone, a pointed version of a cylinder, has 1/3 the volume. This is true also of any pointed objects in which the horizontal dimensions are proportional to the vertical dimensions*. (That is, this formula (1/3Bh), works for any right- or oblique pyramid-like object.)

* in this discussion, we have assumed the base is in a horizontal plane, and the height is measured vertically from that plane. Of course, any orientation is possible.

4 0

3 years ago