Question

If $5-\frac{6}{x}=x$, then x has how many possible values?

• A. None
• B. One
• C. Two
• D. A finite number greater than two
• E. An infinite number

Answer 1

The correct option is C Two

Simplifying Given Equation

$5-\frac{6}{x}=x$

Multiplying By $x$ both sides we get

$\Rightarrow$ $5x-6=x^2$

which can be written as $x^2-5x+6=0$

Now this is of the form of $a{x}^2+bx+c=0$

Therefore, it is a Quadratic Equation

Hence, $x$ can have $2$ values which are the roots of this Quadratic Equation..

Therefore Answer is $\left(C\right)$