All categories

3 years ago

The equation x^3+x^2+ax-4=0 has one root equal to -2. Find the value of a.

Mathematics

1 answer:

Vedmedyk [2.9K]3 years ago

5 0

Answer:

a = - 4

Step-by-step explanation:

Given x = - 2 is a root then f(- 2) = 0

f(x) = x³ + x² + ax - 4, thus

f(- 2) = (- 2)³ + (- 2)² - 2a - 4 = 0, that is

f(- 2) = - 8 + 4 - 2a - 4 = 0, thus

- 8 - 2a = 0 ( add 8 to both sides )

- 2a = 8 ( divide both sides by - 2 )

a = - 4

You might be interested in

Find thhe remainder when 7^203 is divided by 4

Aleksandr [31]

Using the square-and-multiply approach, we have

$7^{203}=7\times(7^{101})^2$
$7^{101}=7\times(7^{50})^2$
$7^{50}=(7^{25})^2$
$7^{25}=7\times(7^{12})^2$
$7^{12}=(7^6)^2$
$7^6=(7^3)^2$
$7^3=7\times7^2$

and so, using the property that, if $a_1\equiv b_1\mod n$ and $a_2\equiv b_2\mod n$ , then $a_1a_2\equiv b_1b_2\mod n$ , we get

$7\equiv3\mod4$
$7^2\equiv9\equiv1\mod4$
$7^3\equiv7\times1\equiv7\equiv3\mod4$
$7^6\equiv9\equiv1\mod4$
$7^{12}\equiv1\mod4$
$7^{25}\equiv7\times1\equiv7\equiv3\mod4$
$7^{50}\equiv9\equiv1\mod4$
$7^{101}\equiv7\times1\equiv7\equiv3\mod4$
$7^{203}\equiv7\times9\equiv3\times1\equiv3\mod4$

4 0

3 years ago

Tatami mats are used as a floor covering in Japan. one possible layout uses four identical rectangular mats and one square mat.

Basile [38]

So by definition, area is equal to the length (x) times the width (y). The area of the square mat is = x × y, or xy
If the area of the rectangular mat is twice that of the square mat, the area of the rectangular mat would have to be = 2 × x × y
This can be written as 2x × y, making the length of the rectangular mat twice that of the square mat's length, and the width the same as the square mat's width.

3 0

3 years ago

Read 2 more answers

How many cm3 is in 1 liter? i just wondering...

natali 33 [55]

Hello,

1 liter of water in normal conditions has a volume of 1dm^3=(1dm)^3=(10 cm)^3=10^3 cm^3=1000 cm^3

4 0

3 years ago

A store buys a digital watch for $80 and sells it for $95 what is the percent of increase

Marina86 [1]

About 1.19 %

80*1.19= 95.2 Since 2 is not 5 or above it get knocks down to 95 exactly

8 0