Friday, 30 July 2021

Given that the equation \((m^2-12)x^4-8x^2-4=0\) has no real roots, then the largest value of \(m\) is \(p\sqrt{q}\), where \(p\) and \(q\) are natural numbers, \(q\) is square-free. Determine \(p+q\).
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Define \(f: \mathbb{R} \rightarrow \mathbb{R}\) by \[f(x)= \begin{cases}(1-\cos x) \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, ...