All categories

3 years ago

Consider that the roots of a cubic equation with integral coefficients are 2, −1, and 4. Which choice is the cubic equation?

Mathematics

1 answer:

Marina86 [1]3 years ago

6 0

The cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Step-by-step explanation:

The roots of the cubic equation are 2,-1 and 4. We need to find the cubic equation.

If 2,-1 and 4 are roots then:

x=2, x=-1 and x=4

or we can write:

x-2=0, x+1=0 and x-4=0

Multiplying the roots to find the cubic equation:

$(x-2)(x+1)(x-4)\\=(x-2)(x(x-4)+1(x-4))\\=(x-2)(x^2-4x+x-4)\\=(x-2)(x^2-3x-4)\\=x(x^2-3x-4)-2(x^2-3x-4)\\=x^3-3x^2-4x-2x^2+6x+8\\Combining\,\,like\,\,terms:\\=x^3-3x^2-2x^2-4x+6x+8\\=x^3-5x^2+2x+8$

So, the cubic equation having roots 2, -1 and 4 is $x^3-5x^2+2x+8$

Keywords: Solving Cubic Polynomial

Learn more about Solving Cubic Polynomial at:

#learnwithBrainly

You might be interested in

8-35. Use your knowledge of polygons to answer the questions below, if possible.

Nataliya [291]

Answer:

(a)I. 13 Sides II. 7 Sides

(b) 4 Sides, Square

(c)x=52 degrees

(d)x=107 degrees

(e)1620 degrees

Step-by-step explanation:

(a)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

I. If the Interior angle is $1980^0$

Then:

$(n-2)180^0=1980^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=11\\$Add 2 to both sides of the equation\\n-2+2=11+2\\n=13$

The polygon has 13 sides.

II. If the Interior angle is $900^0$

Then:

$(n-2)180^0=900^0\\$Divide both sides by 180^0 $ to isolate n$\\n-2=5\\$Add 2 to both sides of the equation\\n-2+2=5+2\\n=7$

The polygon has 7 sides.

(b)The sum of the exterior angle of a polygon is 360 degrees,

Each exterior angle of a n-sided regular polygon is: $\frac{360^0}{n}$

If the exterior angle of a regular polygon is 90°

Then:

$90\°=\frac{360^0}{n}\\ 90n=360\\n=4$

The regular polygon has 4 sides and it is called a Square.

(c)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

Each Interior angle of a regular n-sided polygon is: $\frac{(n-2)180^0}{n}$

For a pentagon, n=5

Then:

$\frac{(5-2)180^0}{5}=2x+4\\108=2x+4\\108-4=2x\\104=2x\\x=52^0$

(d)The sum of the exterior angle of a polygon is 360 degrees.

If four of the exterior angles of a pentagon are 57, 74, 56, and 66.

Let the fifth angle=x

Then:

$57+74+56+66+x=360^0\\253+x=360\\x=107^0$

(e)The Sum of the Interior angle of polygon with n sides is derived using the formula: (n-2)180.

In an 11-gon., n=11

Therefore, the sum of the interior angle=(11-2)180= $1620^0$

The sum of the interior angle does not change either in a regular or irregular polygon.

3 0

3 years ago

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $2.25 and each s

baherus [9]

The equations and the number of hotdogs and sodas sold are: x+ y = 126 and 2.25x + 1.50y = 225.75 ; 49 hot dogs and 77 sodas.

Two equations can be derived from this question:

2.25x + 1.50y = 225.75 equation 1

x + y = 126 equation 2

Where:

x = number of hotdogs sold

y = number of soda sold

In order to determine the value of y, multiply equation 2 by 2.25

2.25x + 2.25y = 283.50 equation 3

Subtract equation 1 from 3

57.75 = 0.75y

y = 77

Substitute for y in equation 2

x + 77 = 126

x = 49

To learn more about simultaneous equations, please check: brainly.com/question/23589883

8 0

3 years ago

Read 2 more answers

)) Omar used 28 centimeters of tape to wrap 4 presents. How much tape will Omar need in

pav-90 [236]

Answer:

He would need 42 cm *or 14cm

Step-by-step explanation:

28/4 is 7

that means that he used 7 cm of tape per present

6 x 7 is 42

that means that he would need 42 cm of tape

4 to 28

6 to 42

*If he already has 4 presents done and he needs to 2 more present then he would need 14 cm, 2 x 7 is 14

8 0

3 years ago

A shirts price was $32, on 6% mark, what is the new price of the shirt

allochka39001 [22]

Answer:

19.20

Step-by-step explanation:

.6 is 6%. X 32

8 0

3 years ago

Read 2 more answers

The total interest on a 5 year 5.2% loan with a principal of $10,000 is 10,000 × 0.052 × 5 = $2,600.

ruslelena [56]

Answer:

truee

Step-by-step explanation:

i had this answer on my test and if i dont get it right sorry

6 0

3 years ago