JoanCarmelCavsidn
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Write the quadratic equation with integer coefficents whose roots are the reciprocal of the roots of 2x^2-3x+1=0...

Sagot :

2x² - 3x + 1 = 0

A)  Solve for the roots.  Solve by factoring:
      2x² - 3x + 1 = 0
      (2x - 1) (x - 1) = 0
      2x - 1 = 0                        x - 1 = 0
      2x - 1 + 1 = 0 + 1            x - 1 + 1 = 0 + 1
      2x = 1                              x₂ = 1
      2x/2 = 1/2                         
      x₁ = 1/2

The roots and their reciprocals are:
x₁ = 1/2        Reciprocal:  x₁ = 2/1  or 2
x₂ = 1           Reciprocal:  x₂ = 1

B) Quadratic equation given the reciprocal of the roots of the first equation:
     x₁ = 2        x₂ = 1

x² - (sum of roots)x + (product of roots) = 0

x² - [(2) + (1)]x + [(2)(1)] = 0

x² - 3x + 2 = 0

ANSWER:  x² - 3x + 2 = 0