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
ElenaW [278]
3 years ago
13

Which correctly describes the roots of the following cubic equation? x3 – 5x² + 3x+9=0

Mathematics
1 answer:
Vikki [24]3 years ago
7 0

Answer:

-1 and 3

Step-by-step explanation:

First, note that there is an evident root in x=-1. You can see this because the coefficients of x3 and x sum the same number than the ones of x2 and the independent term (they sum 4: 1+3=4 and -5+9=4).

We can use this root to apply the Ruffini's rool with all the coefficients:

     1    -5    3   9

-1         -1     6  -9

     1    -6    9   0

This gives as that we can write the equation x3 – 5x² + 3x+9=0 as:

(x+1)*(x2-6x+9) = 0

The first term is due to the root x=-1 and the following is a product of Ruffini's rool. Now we need to find the 2 (at maximum) remaining roots, which are the roots of (x2-6x+9)=0

For this we could use Baskara's formula (you can try it) but lets do something simpler. We know that with the 2 roots, call them a and b, we can write the equation as: (x-a)(x-b)=0

If we apply distributive to (x-a)(x-b) we must get x2-6x+9. So, (-a)(-b) MUST be equal to 9. Working with integers there are not many options. Lets suppose a=b=3:

(x-3)*(x-3)=x2 -3x -3x + 9 = x2 - 6x + 9, and BINGO!

If we didnt get the results we could have tried with a=1 and b=9, for example, and so on. (please, compare with Baskara!).

So, we can write:

x3 – 5x² + 3x+9= (x+1)*(x-3)*(x-3) = (x-1)*(x-3)^2

And the roots are the values that make this equation zero:

x=-1 and x=3 where the last one is a double root.

You might be interested in
Z=Xm+n-p,solve for x
timama [110]

z=xm+n-p

We need to isolate x to one side I will do that on the left side so it looks cleaner, therefore I will first flip the equation.

xm+n-p=z

Now move the n and p to the right side

xm=z-n+p

x=(z-n+p)/m

Hope this helped, if you have any questions about this just comment and I will come answer.

6 0
2 years ago
Write 25x10 to the power of 6 in standard form
Elza [17]

Answer:

25000000 is the correct answer

6 0
2 years ago
In 2007, the population of Ecuador was estimated at
swat32

Answer:

In 2012 , the population will be 15 million

Step-by-step explanation:

We start by setting up an exponential equation that defines the increase

P(t) = I(1 + r)^t

P(t) represents the present population = 15 million

I is the population in 2007 which is 13.8 million

r is 1.6% = 0.016

t is what we want to calculate

15 million = 13.8 million (1 + 0.016)^t

15/13.8 = (1.016)^t

1.09 = (1.016)^t

ln 1.09 = t ln 1.016

t = ln 1.09/ln 1.016

t = 5.429 which is approximately 5

So in 2007 + 5 = 2012, the population will be 15 million

8 0
3 years ago
Solve for j: j + j / 2 + J + 5 = 45
Georgia [21]

Answer:

j:5j/2+5=45 Or j=16 how you put it was a little confusing

5 0
2 years ago
This is to help my wonderful mother. What is 1/3rd of 4 1/2s and 8 1/4s?
crimeas [40]
4 1/2 = 9/2
8 1/4 = 33/4

1/3 x 9/2 = 3/2
1/3 x 33/4 = 33/12
5 0
3 years ago
Other questions:
  • Two Chords, Find X. Need help with this answer as soon as possible.
    9·1 answer
  • Which number line plots the integers –12, –3, and 7? A number line going from negative 15 to positive 10. Points are at negative
    11·2 answers
  • Standard form of y=-5(x+2)(x-3) is
    11·1 answer
  • Please help with geometry,will give brainliest
    15·1 answer
  • What is the solution to the equation: 3 + 5 = 14 Show work.
    12·1 answer
  • To train for a race, Scott's want to run 20 miles this week . he runs 1/4 of the miles on Monday. If he runs 2 miles on Tuesday
    12·1 answer
  • What is [ 4 × ( 4 + 3 ) ] − 3
    5·1 answer
  • Andrew filled a bucket with 7/10 of a gallon of water. A few minutes later, he realized only
    9·2 answers
  • When is it more beneficial to solve a problem involving a proportional relationship using an equation than using a graph?
    9·1 answer
  • Solve question 5 all steps
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!