How do we find u if 3u^3 - u^2 - 6u+ 2= 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The equation to be solved is : 3u^3 - u^2 - 6u+ 2= 0

3u^3 - u^2 - 6u+ 2= 0

=> u^2 ( 3u - 1) - 2(3u - 1) = 0

=> (u^2 - 2)(3u - 1) = 0

u^2 - 2 = 0

=> u^2 = 2

=> u = sqrt 2 and u = -sqrt 2

3u - 1 = 0

=> u = 1/3

The solution of 3u^3 - u^2 - 6u+ 2= 0  is {1/3 , sqrt 2, -sqrt 2}

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the polynomial equation:

3u^3 - u^2 -6u + 2 = 0

First we will factor the equation.

We will factor u^2 from the first 2 terms.

==> u^2 ( 3u - 1) - 6u + 2 = 0

Now we will factor -2 from the last two terms.

==> u^2 ( 3u-1) -2 (3u -1) = 0

Now we will factor (3u-1)

==> (3u-1)( u^2 -2) = 0

Now we will determine the roots.

==> 3u-1 = 0 ==> 3u =1 ==> u= 1/3

==> (u^2-2) = 0 ==> u^2 = 2 ==> u= +-sqrt2

Then we have three roots.

==> u= { 1/3, sqrt2 , -sqrt2}

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