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
GuDViN [60]
3 years ago
6

Solve the equation 2x3 + 7x2 – 10x – 24 = 0 in the real number system.

Mathematics
2 answers:
sladkih [1.3K]3 years ago
5 0

Answer:

x=2 ; x=-4 or x=-3/2

Step-by-step explanation:

We are given a cubic polynomial

2x^3+7x^2-10x-24=0  

Here as we are having a cubic equation to factorize, we have to find some value of x such that when we put that value in place of x , it gives us a 0. We have to try it randomly like first we try it for x=1 then x=2 and so on.

On trying for x=2 , we see that the equation becomes 0=0 and hence x=2 is one of the solution. And also as x=2 is one of the solution, (x-2) must be one of the factor. Now we use this property to determine the other factor like this.

2x^3+7x^2-10x-24=0

Adding and subtracing 4x^2 to 2x^3 we get

2x^3-4x^2+4x^2+7x^2-10x-24=0

Now we take out 2x^2 as GCF

2x^2(x-2)+11x^2-10x-24=0

Now subtracting and adding 22x to 11x^2

2x^2(x-2)+11x^2-22x+22x-10x-24=0

taking 11x^2 as GCF out  

2x^2(x-2)+11x(x-2)+22x-10x-24=0

2x^2(x-2)+11x(x-2)+12x-24=0

2x^2(x-2)+11x(x-2)+12(x-2)=0

Now taking (x-2) out as GCF

(x-2)(2x^2+11x+12)

Now we need to split the middle term of (2x^2+11x+12) to factorize it in such a way that their product is 2*12 and sum is 11. We have 8 and 3 as these factors.

Hence it can be factored like this

(2x^2+11x+12)\\2x^2+8x+3x+12\\2x(x+4)+3(x+4)\\(2x+3)(x+4)

Hence our answer will be

(x-2)(2x+3)(x+4)=0

And thus the solutions will be

x-2=0 : x=2

x+4=0 ; x=-4

2x+3=0 ; x=-\frac{3}{2}

Rom4ik [11]3 years ago
4 0

Answer:

x = 2

x = -4

x = -3/2

Step-by-step explanation:

We need to find the roots of the equation

2x^3 + 7x^2 – 10x – 24 = 0

We can factorize the equation into

(x-2)(x+4)(2x + 3) = 0

Roots

x = 2

x = -4

x = -3/2

The answer to your question is also attached in the images below

You might be interested in
A car is traveling at a speed of 30 miles per hour. What is the car's speed in kilometers per hour? How many kilometers will the
Mandarinka [93]

Answer:

144.84

Step-by-step explanation:

3 0
3 years ago
WILL MARK BRANLIEST IF GOTTEN RIGHT
Mamont248 [21]

Answer:

The last choice. The red one

Step-by-step explanation:

I'm just guessing at this point. But, by the looks of it, red does seem like it would be correct. Again, this is just a guess. So, if it's wrong I'm so sorry. Have a lovely day.

3 0
3 years ago
What is the slope of the line that passes through the points (13,-8) and (-11,4)
pogonyaev

Answer:

- \frac{1}{2}

Step-by-step explanation:

Find slope using the slope formula : \frac{y2-y1}{x2-x1}

Plug in the given points : \frac{4- (-8)}{-11-13}

Add the numbers : \frac{12}{-11-13}

Calculate the difference : \frac{12}{-24}

Reduce the fraction : -\frac{1}{2}

Solution : -\frac{1}{2}

3 0
3 years ago
Anyone want to talk?
Tamiku [17]
Sure you giving points?
5 0
2 years ago
Find the midpoint of AB: A(3,-8) B(-15,-8)
Pavlova-9 [17]

Answer:

C (-6,-8)

good luck buddie

3 0
3 years ago
Read 2 more answers
Other questions:
  • Plz help me with 9,10,and 8
    15·1 answer
  • Which condition must be satisfied in order to use the arc length formula L = the integral from a to b of sqrt(1 + f'(x)^2) dx?
    10·1 answer
  • WILL GIVE BRANLIEST<br> 5(x + 2) over<br> 2x - 14<br> x = 10
    12·1 answer
  • Need help k12 5 math work
    8·2 answers
  • I may be dumb but I still need help
    5·2 answers
  • The population P of a colony of 3600 bacteria at time t minutes can be modeled by the function P(x) = 3600(2)^t/73. How long doe
    12·2 answers
  • What is the equation of the line that passes through the point (−4,−8) and has an undefined slope?
    13·1 answer
  • Help...........Me.........Please......
    11·2 answers
  • PLS HELP
    10·1 answer
  • Question 13
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!