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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.

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.

Grade:

1 Answers

HIBA SHEIKH
29 Points
9 years ago

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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