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
SashulF [63]
1 year ago
7

Solve the following equation. X cubed minus 6X squared plus 6X equals zero

Mathematics
1 answer:
anyanavicka [17]1 year ago
4 0

We have to solve this equation:

x^3-6x^2+6x=0

Third degree polynomials like this one are not easily solved, but this one has a root at x = 0. The let us factorize this polynomial as x times a second degree polynomial:

\begin{gathered} x^3-6x^2+6x=0 \\ x(x^2-6x+6)=0 \end{gathered}

Now we can find the roots of the quadratic polynomial as:

\begin{gathered} x=\frac{-(-6)\pm\sqrt[]{(-6)^2-4\cdot1\cdot6}}{2\cdot1} \\ x=\frac{6\pm\sqrt[]{36-24}}{2} \\ x=\frac{6\pm\sqrt[]{12}}{2} \\ x=\frac{6\pm\sqrt[]{4\cdot3}}{2} \\ x=\frac{6\pm2\sqrt[]{3}}{2} \\ x=3\pm\sqrt[]{3} \\ x_1=3-\sqrt[]{3} \\ x_2=3+\sqrt[]{3} \end{gathered}

Then, the solutions to the equation are:

x = 0

x = 3 - √3

x = 3 + √3

You might be interested in
Jamie rented a canoe while she was on vacation. She paid a flat $85.00 plus $7.50 each day. Her total cost was $130.00. For how
mixer [17]
She rented the canoe for 6 days.
6 0
2 years ago
Read 2 more answers
Help plz. Ignore the orange around the choice.
VMariaS [17]

Answer:

May I suggest -11

Step-by-step explanation:

4 0
3 years ago
When x=8,y=20.find y when x=20
Deffense [45]

20/8 = 2.5

20 * 2.5 = 50

x = 8 * 2.5

y = 20 * 2.5

When x = 20, y = 50

6 0
3 years ago
Read 2 more answers
Micah went to the grocery store the other day and there were no price tags on anything! She bought 3 loaves of bread and 1 milk
NARA [144]

Answer:

$2.75

Step-by-step explanation:

We know that the random persons total was $5.50. To figure out how much one loaf of bread costs we must first, divide $5.50 by 2. We get 2.75. Then, to double check our answer we multiply that by 3 to get 8.25. We know that Micah' s total was $9.00. 9 minus 8.25 equals 0.75.

That price is very reasonable, for a jug of milk, so we know that $2.75 is the answer.

<em>Hope this helped</em><em> </em><em> </em><em>:</em><em>)</em>

6 0
3 years ago
25 points volume math answer clue pls ty
Vikentia [17]

Answer:

my guy did you repost this as I just answered this about ten minutes ago

4 0
3 years ago
Read 2 more answers
Other questions:
  • Find all solutions of sqrt(3)tan(3x) = 0
    12·1 answer
  • Lupita brought seven pounds of pretzels at a local wholesaler for 16.80 her friend Charles about 5 pounds of pretzels at the sup
    15·1 answer
  • Which procedure justifies whether Negative 3 x (5 minus 4) + 3 (x minus 6) is equivalent to Negative 12 x minus 6? The expressio
    6·2 answers
  • 100 pencils cost 7.00 1 pencil cost
    12·2 answers
  • Ashley read 30 pages last night in 20 minute. How many pages will she have read after 2 hours?
    10·2 answers
  • A newspaper article indicated that 43 percent of cars with black seats are white, 46 percent of cars with black seats are blue,
    7·2 answers
  • Please help, last question ill probably ask on here HELP. Name the pair with the number so ik which one it is for ​
    12·1 answer
  • Find the solution for quadratic x^2-7x+10=-2 leave your answers as fractions ( no decimals)
    12·1 answer
  • [2] + [-13]= <br>please help me!!!​
    6·2 answers
  • 25x + 10y = 600<br> 5x - 3y = 70
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!