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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.

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You notice a hot air balloon descending. The elevation h (in feet) of the balloon is modeled by the function h(x)=−11x+330, wher

Mars2501 [29]

Answer:

1) Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

2) The slope of the given equation, shows that the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

Step-by-step explanation:

1) The function modelling the height of the balloon is h(x) = -11x + 330

Where;

x = The time of elevation of the balloon

The data for the graphing derived from Microsoft Excel are as follows

x ${}$ h(x)

0 ${}$ 330

5 ${}$ 275

10 ${}$ 220

15 ${}$ 165

20 ${}$ 110

25 ${}$ 55

30 ${}$ 0

Please find attached, the graph of the function

The domain of the function is 0 ≤ x ≤ 30

The range of the function is 330 ≥ x ≥ 0

Comparing the given function to the general equation of a straight line, y = m·x + c, we have that the slope, m = -11

2) The slope of a straight line graph gives the rate of change of the dependent variable, per unit change in the independent variable

Therefore, the slope of the given equation, -11 gives the rate of change of the function per unit increase in the independent variable x

Therefore, the elevation decreases, by (-)11 feet for each increase in time by one second

3) The y-intercept gives the initial elevation of the balloon at time t = 0 seconds

The x-intercept gives the final elevation of the balloon when it lands at time t = 30 seconds

8 0

2 years ago

Read 2 more answers

Find all solutions of each equation on the interval 0 ≤ x < 2π.

Korvikt [17]

Answer:

$x = 0$ or $x = \pi$ .

Step-by-step explanation:

How are tangents and secants related to sines and cosines?

$\displaystyle \tan{x} = \frac{\sin{x}}{\cos{x}}$ .

$\displaystyle \sec{x} = \frac{1}{\cos{x}}$ .

Sticking to either cosine or sine might help simplify the calculation. By the Pythagorean Theorem, $\sin^{2}{x} = 1 - \cos^{2}{x}$ . Therefore, for the square of tangents,

$\displaystyle \tan^{2}{x} = \frac{\sin^{2}{x}}{\cos^{2}{x}} = \frac{1 - \cos^{2}{x}}{\cos^{2}{x}}$ .

This equation will thus become:

$\displaystyle \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} \cdot \frac{1}{\cos^{2}{x}} + \frac{2}{\cos^{2}{x}} - \frac{1 - \cos^{2}{x}}{\cos^{2}{x}} = 2$ .

To simplify the calculations, replace all $\cos^{2}{x}$ with another variable. For example, let $u = \cos^{2}{x}$ . Keep in mind that $0 \le \cos^{2}{x} \le 1 \implies 0 \le u \le 1$ .