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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.
