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

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

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

Step-by-step explanation:

We are given a cubic polynomial

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.

Adding and subtracing to we get

Now we take out as GCF

Now subtracting and adding to

taking as GCF out  

Now taking out as GCF

Now we need to split the middle term of 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

Hence our answer will be

And thus the solutions will be

x-2=0 : x=2

x+4=0 ; x=-4

2x+3=0 ; x=-