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

Question

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

If the roots of the quadratic equation `4p-p^2-5x^2-(2p-1)x+3p=0` lie on either side of unit, then the number of interval values of `p` is `1` b. `2` c. `3` d. 4
A. 1
B. 2
C. 3
D. 4

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - 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.