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What is the solution of 12x^3-14x^2+2=0

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xetaalpha | Student | (Level 2) Honors

Posted February 19, 2012 at 3:10 AM via web

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What is the solution of 12x^3-14x^2+2=0

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted February 19, 2012 at 3:17 AM (Answer #1)

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The equation 12x^3-14x^2+2=0 has to be solved. Use factorization to find the roots.

12x^3-14x^2+2=0

=> 12x^3 - 6x^2 - 8x^2 + 4x - 4x + 2 = 0

=> 6x^2(2x - 1) - 4x(2x - 1) - 2(2x - 1) = 0

=> (2x - 1)(6x^2 - 4x - 2) = 0

=> (2x - 1)(6x^2 + 2x - 6x - 2) = 0

=> (2x - 1)(2x(3x + 1) - 2(3x + 1)) = 0

=> (2x - 1)(2x - 2)(3x + 1) = 0

x = 1/2, x = 1 and x = -1/3

The solution of the equation 12x^3-14x^2+2=0 is x = -1/3, x = 1/2 and x = 1

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