All categories

2 years ago

K(x) = x^3 +2x^2-x-2 find all roots

Mathematics

1 answer:

Liono4ka [1.6K]2 years ago

3 0

<h2>The all roots are equation are 1, - 1 and - 2.</h2>

Step-by-step explanation:

The given cubic polynomial:

k(x) = $x^3$ + 2 $x^2$ - x -2

To find, the all roots are $x^3$ + 2 $x^2$ - x -2 = ?

∴ k(x) = $x^3$ + 2 $x^2$ - x -2

⇒ $x^3$ + 2 $x^2$ - x -2 = 0

⇒ $x^2$ (x + 2) - 1(x + 2) = 0

⇒ ( $x^2$ - 1)(x + 2) = 0

⇒ $x^2$ - 1 = 0 and x + 2 = 0

⇒ $x^2$ - 1 = 0

⇒ $x^2$ = 1

⇒ x = ± 1 = 1, - 1

or, x + 2 = 0

⇒ x = - 2

Thus, the all roots are equation are 1, - 1 and - 2.

You might be interested in

The area of the rectangle shown below is 6x2+11x-7 square units. the length is 2x-1 what is the width

Hitman42 [59]

Answer:

Width is 3x+7 units

Step-by-step explanation:

In the attached file

5 0

2 years ago

Read 2 more answers

Please show work!!!!!!!

kolezko [41]

Answer:

Step-by-step explanation:

The cylindrical part

Area of the cylindrical part = Circumference of the circle * height

Area of the cylindrical part = pi * d * height

Area = 3.14 * 10 * 9

Area = 282.6

Lid

Area = pi * r^2

r = 5

Area = 3.14* 5^2 * 2

Area = <u> 157</u>

Total 439.6

I know this doesn't look right according to the diagram, but it is the only way that you can solve the question. That is, you must assume there are two lids, not one as the diagram suggests.

4 0

2 years ago

Marine biologists have determined that when a shark detectsthe presence of blood in the water, it will swim in the directionin w

siniylev [52]

Solution :

a). The level curves of the function :

$C(x,y) = e^{-(x^2+2y^2)/10^4}$

are actually the curves

$e^{-(x^2+2y^2)/10^4}=k$

where k is a positive constant.

The equation is equivalent to

$x^2+2y^2=K$

$\Rightarrow \frac{x^2}{(\sqrt K)^2}+\frac{y^2}{(\sqrt {K/2})^2}=1, \text{ where}\ K = -10^4 \ln k$

which is a family of ellipses.

We sketch the level curves for K =1,2,3 and 4.

If the shark always swim in the direction of maximum increase of blood concentration, its direction at any point would coincide with the gradient vector.

Then we know the shark's path is perpendicular to the level curves it intersects.

b). We have :

$\triangledown C= \frac{\partial C}{\partial x}i+\frac{\partial C}{\partial y}j$

$\Rightarrow \triangledown C =-\frac{2}{10^4}e^{-(x^2+2y^2)/10^4}(xi+2yj),$ and

$\triangledown C$ points in the direction of most rapid increase in concentration, which means $\triangledown C$ is tangent to the most rapid increase curve.