Question

Use the x-intercept method to find all real solutions of the equation. 14x^3-53x^2+41x-4=-4x^3+x^2+x+4

Answer 1

Given 14x^3-53x^2+41x-4=-4x^3+x^2+x+4
18x^3-54x^2+40x-8=0
let (x-2) is one of the factor
use long division of (x-2) into 18x^3-54x^2+40x-8
left with
9x^2-9x+2
9x^2-6x-3x+2
3x(3x-2)-1(3x-2)
(3x-2)(3x-1)
hence
x=2
x=1/3
x=2/3

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