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3 years ago

How many real number solutions does the equation x3 + 5x2 + 3x – 9 = 0 have?

2 answers:

8 0

F(x) = x³ + 5x² + 3x - 9 = 0
There is 1 sign change in f(x), so there is 1 positive real root.

f(-x) = -x³ + 5x² - 3x - 9
There are 2 sign changes in f(-x), so there are either
(a) 2 negative real roots, or
(b) a pair of complex roots.

Use the Remainder Theorem to test for the positive real root.
f(1) = 1 + 5 + 3 - 9 = 0
Therefore (x-1) is a factor of f(x).

Perform synthetic division.
1 | 1 5 3 -9
1 6 9
---------------
1 6 9 0

f(x) = (x-1)(x² + 6x + 9) = (x-1)(x+3)²
The zeros or roots are 1, -3, -3.
Therefore there are 3 real solutions for f(x) = 0.

Answer: 3 real solutions

likoan [24]3 years ago

6 0

Answer:

Step-by-step explanation:

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The area of the rectangle is 6 square feet. If its width is 2 1/7<br> feet, find its length.

densk [106]

Answer:

L = 2 4/5 feet

Step-by-step explanation:

A = L x W

6 = L x 2 1/7

divide both sides by 2 1/7

6 divided by 2 1/7 = L (is the same as multiplying by the reciprocal)

6 x 7/15 = L

L = 14/5 or 2 4/5

5 0

3 years ago

When the product of 6 and the square of a number is increased by 5 times the number, the result is 4.

il63 [147K]

Let $x$ be the unknown number. Its square is $x^2$ . The product of 6 and the square of the number is $6x^2$ . Increase this by 5 and you get $6x^2+5$ .

If this has to equal 4, you have $6x^2+5=4$

4 0

3 years ago

Read 2 more answers

Next, you will make a scatterplot. Name a point that will be on your scatterplot and describe what it represents.

klio [65]

The point (12, 190) means that the temperature after 12 hours is 190 degrees Celsius

<h3>How to make a scatter plot?</h3>

To do this, we make use of the following points

(12, 190), (14, 201), (15, 301), (16, 305), (18, 350), (20, 40), (25, 450)

Where x represents the number of hours and y represents temperature

See attachment for the scatter plot.

<h3>The description of a point</h3>

To do this, we make use of the point (12, 190)

This means that the temperature after 12 hours is 190 degrees Celsius

Read more about scatter plots at:

brainly.com/question/13984412

#SPJ1

8 0

2 years ago

What is an equation of the line that passes through the points ( 0,-7) and ( 5, -1)

tresset_1 [31]

Answer:

y = 5/6x - 5.167

y = 5/6x - 31/6

Step-by-step explanation:

The equation of a line

y = mx + c

Step 1: find the slope

m = y2 - y1 / x2 - x1

Given points

( 0 , -7) ( 5 , -1)

x1 = 0

y1 = -7

x2 = 5

y2 = -1

Insert the values into the equation

m = -1 - (-7) / 5 - 0

m = -1 + 7 / 5

m = 6/5

y = 6/5x + c

Step 2: sub any of the two points given into the equation

y = 5/6x + c

( 5 , -1)

x = 5

y = -1

-1 = 5/6(5) + c

-1 = 5*5/6 + c

-1 = 25/6 + c.

c = -1 - 25/6

LCM = 6

c = -6 - 25 / 6

c = -31/6

c = -5.167

Step 3: sub c into the equation

y = 5/6x + c

y = 5/6x - 31/6

y = 5/6x - 5.167

The equation of the line is

y = 5/6x - 5.167

7 0

3 years ago

The diagram below shows a triangle with base (x+5) and height 2x inside a shaded rectangle with length (3x+1) and width (3x-5).

Ilya [14]

Answer:

3 for the first one 2ed one is 5

Step-by-step explanation:

6 0

3 years ago