All categories

3 years ago

Find all zeros of f(x)= x^3-4x^2-5x+20

1 answer:

5 0

Possible roots are the factors of 20: {1, 2, 4, 5, 10, 20} and their negatives.

Use synthetic division. For example, if I chose 4 as a possible root, the synthetic division setup would be

____________
4 / 1 -4 -5 20
4 0 -20
_____________
1 0 -5 0

This tells us that 4 is a root (I was just lucky) and (x-4) is a factor.

The quotient (remaining factor) is (x^2 - 5), which, if factored, yields

x = sqrt(5) and x = -sqrt(5)

In summary, the roots (or zeros) of <span>f(x)= x^3-4x^2-5x+20 are
{sqrt(5), -sqrt(5), 4}</span>

You might be interested in

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

9966 [12]

Answer:

$(a)\ Area = 3765.32$

$(b)\ Area = 4773$

Step-by-step explanation:

Given

$A_1 = 169in^2$ --- area of each square

$Shade = 4in$

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

$L^2 = A_1$

$L^2 = 169$

$L = \sqrt{169$

$L=13$

The length of two squares make up the radius of the semicircle.

So:

$r = 2 * L$

$r = 2*13$

$r = 26$

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

$A_2 = 16 * 169$

$A_2 = 2704$

The area of the semicircle is:

$A_3 = \frac{\pi r^2}{2}$

$A_3 = \frac{3.14 * 26^2}{2}$

$A_3 = 1061.32$

So, the area of the window is:

$Area = A_2 + A_3$

$Area = 2704 + 1061.32$

$Area = 3765.32$

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

$Length = 4 * 13 + 8$

$Length = 60$

$Height = 4*13 + 4$

$Height = 56$

The area is:

$A_1 = 60 * 56 = 3360$

The radius of the semicircle becomes initial radius + 4

$r = 26 + 4 = 30$

The area is:

$A_2 = \frac{3.14 * 30^2}{2} = 1413$

The area of the shade is:

$Area = A_1 + A_2$

$Area = 3360 + 1413$

$Area = 4773$

7 0

2 years ago

A 7000.00 principal is invested in 2 accounts, 1 earning 3%interest the other 7% interest with the total interest for the year 2

MakcuM [25]

Answer:

The amount in the first account is $5,700

The amount in the second account is $1,300

Step-by-step explanation:

Let the mount invested in the first account be $x$ and the one invested in the second account be $y$ .

Then the total principal is $x+y=7000$ ---->(1)

The interest in the first account is $.03*x$

The interest in the first account is $.07*y$

The total interest for the year is 262.00.

This implies that:

$0.03x+0.07y=262$ ---->(2)

We solve the two equations simultaneously to get:

$x=5,700$ and $y=1,300$

7 0

3 years ago

I need help pls answer right away

Zielflug [23.3K]

Answer:

Step-by-step explanation:numerator divided by denominator???

6 0

2 years ago

Read 2 more answers

If x divided 9=9 how do u know what x is

Volgvan

X is 1 because if you times it by x it equals it number

7 0

3 years ago

Read 2 more answers

Pls help with asap thxxu! :)

Stella [2.4K]

Answer:

C- Equilateral triangle

Step-by-step explanation:

I am not very sure dear

7 0

3 years ago

Read 2 more answers