# An algebra problem by anandmay patel

Algebra Level 3

A function $$f(x)$$ is such that it outputs values by computing the inputs through some quadratic methods. Also, the output for a variable $$x$$ can be given in some form of a polynomial. Now, we know that $$f(5)=0$$ and $$f(0)=5$$. The function gives the output as zero for only one (unique) input. The graph of the function touches the $$x$$-axis at point $$w$$ and cuts the $$y$$-axis at point $$q$$. Find the $$\textbf{length}$$ of line $$wq$$.

Note: In the answer options, $$y = 0.5 \log_{10} 2 + \log_{10} 5$$

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