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

Help me with my math homework please.

MariettaO [177]

Answer:

look around the bottom of the page and if it has something like a brand or company whatever write it down in the search and then write the title of the paper and look for pdfs

5 0

2 years ago

Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans

Valentin [98]

Answer:

1. $2r+1.6b=10$

2. $r=5-0.8b$

3. $b=6.25-1.25r$

Step-by-step explanation:

<h3> The complete exercise is: "Brown rice costs $2 per pound, and beans cost $1.60 per pound. Lin has $10 to spend on these items to make a large meal of beans and rice for a potluck dinner. Let b be the number of pounds of beans Lin buys and r be the number of pounds of rice she buys when she spends all her money on this meal.</h3><h3>1. Write an equation relating the two variables.</h3><h3>2. Rearrange the equation so "b" is the independent variable.</h3><h3>3. Rearrange the equation so "r" is the independent variable."</h3><h3 />

1. According to the information exercise given in the exercise, the cost per pounds of brown rice is $2. Since "r" represents the number of pounds of rice Lin buys, the total cost of the brown rice she buys can be represented with this expression:

$2r$

The beans cost $1.60 per pound. Since "b" represents the number of pounds of beans Lin buys, the total cost of beans she buys can be represented as:

$1.6b$

Knowing that she spends $10, you can write the following equation:

$2r+1.6b=10$

2. In order to rearrange the equation so "b" is the independent variable, you need to solve for "r":

$2r+1.6b=10\\\\2r=10-1.6b\\\\r=\frac{10-1.6b}{2} \\\\r=5-0.8b$

3. To rearrange the equation so "r" is the independent variable, you must solve for "b". You get:

$2r+1.6b=10\\\\1.6b=10-2r\\\\b=\frac{10-2r}{1.6}\\\\b=6.25-1.25r$

7 0

2 years ago

Two of the angles in a triangle measure 52 and 22 what must be the measure of the third angle

viktelen [127]

The measure of the third angle is 74

7 0

2 years ago

Answer asap thank you!??!!??!

Semenov [28]

The answer to the problem is A

7 0

2 years ago

what is the answer here 90 student went to the zoo, 3 had hamburger milk and cake; had 5 milk and hamburger; 10 had cake and mil

dangina [55]

Answer:

a) 37

b) 2

c) 17

d) 8

Step-by-step explanation:

90 Students went to the zoo. 3 had hamburger, milk and cake; 5 had milk and hamburger, 10 had cake and milk; 8 had cake and hamburger; 24 had hamburger; 38 had cake; 20 had milk. How many had a. nothing b. cake only c. milk only d. hamburger only

Solution:

Let h represent students that ate hamburger, m represent students that had milk and c represent students that had cake.

Given that:

n(h ∩ m ∩ c) = 3, n(m ∩ h) = 5, n(c ∩ m) = 10, n(c ∩ h) = 8, n(h) = 24, n(c) = 38, n(m) = 20

The number of students that had nothing = n(h ∪ m ∪ C)'

The number of students that had only milk = n(m ∩ h' ∩ C')

The number of students that had only cake = n(m' ∩ h' ∩ C)

The number of students that had only hamburger = n(m' ∩ h ∩ C')

a) n(m ∩ h' ∩ C') = n(m) - n(m ∩ h) - n(c ∩ m) - n(h ∩ m ∩ c) = 20 - 5 - 10 - 3 = 2

n(m' ∩ h ∩ C') = n(h) - n(m ∩ h) - n(c ∩ h) - n(h ∩ m ∩ c) = 24 - 5 - 8 - 3 = 8

n(m' ∩ h' ∩ C) = n(m) - n(m ∩ c) - n(c ∩ h) - n(h ∩ m ∩ c) = 38 - 10 - 8 - 3 = 17

n(m ∩ h' ∩ C') + n(m' ∩ h ∩ C') + n(m' ∩ h' ∩ C) + n(h ∪ m ∪ C)' + n(h ∩ m ∩ c) + n(m ∩ h) + n(c ∩ m) + n(c ∩ h) = 90

2 + 8 + 17 + 5 + 10 + 8 + 3 + n(h ∪ m ∪ C)' = 90

53 + n(h ∪ m ∪ C)' = 90

n(h ∪ m ∪ C)' = 37

b) n(m' ∩ h' ∩ C) = 17

c) n(m ∩ h' ∩ C') = 2

d) n(m' ∩ h ∩ C') = 8

4 0

2 years ago