Solve using the quadratic formula:3x^2 - 4x + 3 = 0

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justaguide | College Teacher | (Level 2) Distinguished Educator

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For a quadratic equation ax^2 + bx + c = 0, the roots are given by x1 = [-b + sqrt (b^2 - 4ac)]/2a and x1 = [-b - sqrt (b^2 - 4ac)]/2a

Here the equation given is 3x^2 - 4x + 3 = 0

a = 3 , b = -4 and c = 3

x1 = [-b + sqrt (b^2 - 4ac)]/2a

=> [4 + sqrt (16 - 36)]/6

=> 2/3 + i*sqrt (20)/6

=> 2/3 + i*(sqrt 5)/3

x2 = 2/3 - i*(sqrt 5)/3

The roots of the equation are 2/3 + i*(sqrt 5)/3 and 2/3 - i*(sqrt 5)/3

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

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Given the quadratic equation:

3x^2 - 4x + 3 = 0

We will use the quadratic formula to solve for x.

==> x = [ -b + sqrt(b^2-4ac)]/2a

==> a = 3     b= -4     c= 3

==> x1= [ 4+sqrt(16-4*3*3)]/2*3

             = [ 4+ sqrt(-20) / 6

              = 4+ 2sqrt5*i)/ 6

              = ( 2+ sqrt5*i)/3

==> x2= (2-sqrt5*i)/3

Then we have two complex roots.

==> x = { (2+sqrt5*i)/3  ,    (2-sqrt5*i)/3  }

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