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Find all the values of p for which one root of the equation x^2 - (p+1)x + (p^2 + p - 8 )= 0 is greater than 2 and the other root is smaller than 2.
let, f(x)=x2-(p+1)x+(p2+p-8)=0
sincr on root of f(x) is greater than 2 and the other root is greater than 2,
the required conditionis f(2)<0
therefore, f(2)= 4-2(p+1)+(p2+p-8)<0
=> p2-p-6<0
=> (p+2)(p-3)<0
=> p belongs to (-2,3) (answer)
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