Verify that 1/2,1,2 are the zeros of quadratic polynomial 2x cube+2x square-3x+2,and then verify the relationship between the zeros and the coefficients

Question

^{find relationship and verify in alpha beta gama}

Answer 1

1/2, 1, and 2 are not zeros and the polynomial is cubic, not quadratic.

 

2x^3 + 2x^2 - 3x + 2 = 0  is what you have given.

 

-2 is a solution, as 2(-8) + 2(4) - 3(-2) + 2 = 0

 

Using synthetic division:

 

-2 |   2    2      -3      2

              -4     4     -2

   -----------------------------

        2    -2     1   0

 

2x^2 - 2x + 1  is the resulting quadratic.

 

By quadratic formula:

 

x = [2 +or-  sqrt(  (-2)^2  - 4(2)(1) )] / 4

 

  =  [ 2 +or- sqrt(  4 - 8) ] / 4

 

  = 2 +or- sqrt(-4) ] / 4

 

  = [2 +or- 2i ]/4

 

 =  [ 1 +or- i ]/2

 

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