Question

Solve the following equations
12x³ + 8x = 29x² – 4 = 0

Answer 1

12x³ + 8x = 29x² – 4

12x³ – 29x² + 8x + 4 = 0  ......(1)

By Trail and error method, (x – 2) is a factor of (1)

The other factor is 12x² – 5x – 2

The roots is 12x² – 5x – 2 = 0

(3x – 2)(4x + 1) = 0

x = `2/3`, x = `- 1/4`

The roots are `2, 2/3, - 1/4`

Here a_n = 12, a₀ = 4

Let `"p"/"q"` be the root of the equation (1)

The factors of a₀: ±1, ±2, ±4 .....(P must divisible by 4)

The factor of a_n: ±1, ±2, ±3, ±4, ±6, ±12

q must divide as (12)

Using these p and q we can form

`+-  1, +-  2, +- 1/2, +- 2/3, +- 1/6, +- 1/4, +- 3/4, +- 3` are the possible roots of equation (1)