If the roots of the equation \(px^2-40x+96=0\) are even integers, then what is the value of \(p\)?
4
Since the roots are even integers, let them be \(2a\) and \(2b\). Testing \(p=4\), the equation becomes \(4x^2-40x+96=0 \Rightarrow x^2-10x+24=0 \Rightarrow (x-4)(x-6)=0\), giving roots \(x=4,6\), both even integers. No smaller value of p (1, 2 or 3) yields integer roots. Hence \(p=4\).
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