E-DR04 · Roots on opposite sides of a chosen value
Let \(f_p(x)=x^2-2px+p+3\), where \(p\) is real.
Find all \(p\) for which \(f_p(x)=0\) has two distinct real roots.
Find \(p\) for which \(x=1\) is a root.
Find all \(p\) for which one root is less than 1 and the other is greater than 1. Justify that your condition is sufficient.
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