Question

Solve the equation 2x^3 +7x^2 -10x-24=0. Hence solve the equation 2z^3 -7z^2-10z+24 = 0.

Answer 1

In case it was unclear:
Solve the equation \[2x ^{3}+7x ^{2}-10x-24=0\]
and hence solve the equation
\[2z ^{3}-7z ^{2}-10z+24=0\]

Answer 2

using a suitable substitution

Answer 3

help @ganeshie8

Answer 4

what kind of substitutions have you used in the past.
To solve this kind of problem i would use rational roots theorem, and if that doesn't work a computer algebra system.

Answer 5

do you go to agora? @pythagoras123

Answer 6

@BriellShaw no

Answer 7

oh nvm i see that you are in college

Answer 8

Are you in college??

Answer 9

$$2x ^{3}+7x ^{2}-10x-24=(x-2)(2x+3)(x+4)$$

Answer 10

you can set those factors individually to zero

Answer 11

Example of substitution would be
Solve the equation \[2x ^{3}+7x ^{2}-10x-24=0\]
Hence solve the equation \[2(y+2)^{3} +7(y+2)^{2}-10y-44=0\]
The second equation can be written as \[2(y+2)^{3}+7(y+2)^{2}-10(y+2)-24=0\]
Hence substituting x as (y+2)

Answer 12

Thing is, I don't know how to do the substitution for the specific equation I listed

Answer 13

There are substitutions used to solve cubic equations.

Answer 14

I was looking at this
http://home.scarlet.be/math/cubic.htm