How would i solve these math questions?

Question

(a) The equation 12x^3 − 23x^2 − 3x + 2 = 0 has a solution x = 2. Find all other solutions.

(b) Solve for x, the equation 12x^3 + 8x^2 − x − 1 = 0. (All solutions are rational and between ±1.)

Answer 1

Hi,

iterate these questions

I am gonna do the second one for you, do the first one yourself ok.

12x^3 + 8x^2 − x − 1 = 0

=> 12x^3 + 8x^2 − 1 = x

=> x = 12x^3 + 8x^2 − 1

Now put the value of x = 1 on the RHS and the whatever the answer comes out, put it on the RHS and keep on doing so until you have RHS and LHS equal.

i.e., x = 1

x = 19

x = 85,195

x = 7.42 * 10 ^15

so this is not converging,

now try x = -1 as initial guess

=> x = -1

x = -5

x = -1301

x = -2.64*10^10

so this is not converging either

This question has no solution within ±1. I think you have entered the question wrong.

Answer 2

Check if x=2 is a solution;then this equation must be dividable to(x-2)

,then you have (x-2)(12x^2 + x -1)=0,then you have,

(x-2)(4x-1)(3x+1)=0,other answers are x=1/4 & x=-1/3