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If the roots of the quadratic equation `(4p-p^2-5)x^2-(2p-1)x+3p=0` lie on either side of unity, then the number of integral values of `p` is

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Since the coefficient of `n^(2)=(4p-p^(2)-5)lt0`
Therefore the graph is open downward.
According to the question 1 must lie between the roots.
Hence `f(1)gt0`
`implies4p-p^(2)-5-2p+1+3pgt0`
`implies-p^(2)+5p-4gt0`
`impliesp^(2)-5p+4lt0`
`implies(p-r)(p-1)lt0`
`implies1ltplt4`
`:.p=2,3`
Hence, number of integral values fo `p` is 2.
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