1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Kobotan [32]
3 years ago
15

​Find all roots: x^3 + 7x^2 + 12x = 0 Show all work and check your answer.

Mathematics
1 answer:
Aliun [14]3 years ago
4 0

The three roots of x^3 + 7x^2 + 12x = 0 is 0,-3 and -4

<u>Solution:</u>

We have been given a cubic polynomial.

x^{3}+7 x^{2}+12 x=0

We need to find the three roots of the given polynomial.

Since it is a cubic polynomial, we can start by taking ‘x’ common from the equation.

This gives us:

x^{3}+7 x^{2}+12 x=0

x\left(x^{2}+7 x+12\right)=0   ----- eqn 1

So, from the above eq1 we can find the first root of the polynomial, which will be:

x = 0

Now, we need to find the remaining two roots which are taken from the remaining part of the equation which is:

x^{2}+7 x+12=0

we have to use the quadratic equation to solve this polynomial. The quadratic formula is:

x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}

Now, a = 1, b = 7 and c = 12

By substituting the values of a,b and c in the quadratic equation we get;

\begin{array}{l}{x=\frac{-7 \pm \sqrt{7^{2}-4 \times 1 \times 12}}{2 \times 1}} \\\\{x=\frac{-7 \pm \sqrt{1}}{2}}\end{array}

<em><u>Therefore, the two roots are:</u></em>

\begin{array}{l}{x=\frac{-7+\sqrt{1}}{2}=\frac{-7+1}{2}=\frac{-6}{2}} \\\\ {x=-3}\end{array}

And,

\begin{array}{c}{x=\frac{-7-\sqrt{1}}{2}} \\\\ {x=-4}\end{array}

Hence, the three roots of the given cubic polynomial is 0, -3 and -4

You might be interested in
Plz helpppp I don’t GET THIS
Liono4ka [1.6K]
First you have to find 1/3 of the marbles. That means in the twelve marvels she has, there are three even groups. Divide twelve by three and you get four. So if each group is four, it is simple from here on out. If she started out with twelve and she lost 1/3 of them(4) it would be 12-4. You know this because lost is another for for subtract. 12-4=8. She has 8 marbles left.
6 0
3 years ago
Read 2 more answers
A restaurant cook uses 5 quarts of turkey soup to fill out 9 bowls. Each bowl contains the same amount of soup. How much soup is
kolbaska11 [484]
9/5 or 1 4/5 quarts ( sorry if wrong )
5 0
3 years ago
Read 2 more answers
Tim needs 18 pens he can buy them in packages of 6 9 or 12 he will buy only one type of package which packages could Tim buy wri
emmainna [20.7K]

Answer:

See below.

Step-by-step explanation:

Either 3 packets of 6 pens  or

2 packets of 9 pens.

3 0
3 years ago
Read 2 more answers
Graph the line that has slope 1/2 and y intercept (0,-1).
puteri [66]

Answer: I added an attachment of what the graph should look like! :)

Step-by-step explanation:

5 0
2 years ago
You are ordering DVD's from a web site. They charge $14 for each DVD. For any order you must pay an additional $6 for shipping a
valkas [14]

Answer:

y = 16x + 6

Step-by-step explanation:

They charge $14 for each DVD, which mean the slope of the function is 14

You must pay an additional $6 for shipping and handling, which means no matter how many DVD you buy, you have to pay a flat fee for $6  

So our function is:

y = 16x + 6 where:

y is total cost

x is the number of DVD you buy (x>0)

5 0
3 years ago
Other questions:
  • Chuck bought new tires for the nerd herd company car that are guaranteed for 42,000 miles. If he drives 11.5 miles each way to w
    9·1 answer
  • Gabriella expects to earn $50 in tips during her shift as a waitress today. In addition to tips, she earns $8.00 an hour. If she
    7·2 answers
  • Show all work to factor x4 − 17x2 + 16 completely.
    13·1 answer
  • what is the missing number? imput B;4,12,16,24,32,40. output A:8,16,20,_,_ rules a=b+4. SUPER URGENT !!!!!!!!!!
    12·1 answer
  • See geometry question above.
    9·1 answer
  • If a = b, then a - c = b - c. This is the _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ property of equality.
    9·2 answers
  • Does anybody know the answer to (-6)(2)+(-8\4
    9·2 answers
  • Clara and Miles each improved their yards by planting
    14·1 answer
  • Write a SIMPLIFIED inequality for x that would give a rectangle with a length of 4 meters and a width of x+7 meters an area of m
    11·1 answer
  • 88888*88888 help me please
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!