SOLUTION: What is the standard form, discriminant and nature of the roots of the equation 1/x

SOLUTION: What is the standard form, discriminant and nature of the roots of the equation 1/x - x/6 = 2/3 ?

Question 1186583: What is the standard form, discriminant and nature of the roots of the equation 1/x - x/6 = 2/3 ?
Answer by ikleyn(52751) (Show Source): You can put this solution on YOUR website!
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What is the standard form, discriminant and nature of the roots of the equation 1/x - x/6 = 2/3 ?
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The starting equation is 

     -  = .


Multiply both sides by 6x;  then transform to the standard form.


    6 - x^2 = 4x

    x^2 + 4x - 6 = 0.


The last equation is in the standard form.


The discriminant is  " b^2 - 4ac " = 4^2 - 4*1*(-6) = 16 + 24 = 40.


The discriminant is positive;  hence, the roots of this quadratic equation are real numbers.


So, the roots of the original equation are real numbers, too.

Solved and answered.

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