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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