if the roots of the quadratic equation `(4p - p^(2) - 5)x^(2)` ` - 2mx + m^(2) - 1 = 0` are greater then - 2 less then 4 lie in the interval

Options

A. 1
B. 2
C. 3
D. 4

Answer

2

Explanation

Note that coefficient of `x^(2) is (4p - p^(2) - 5) lt 0 ` . Therefore, the
graph is concave downward . According to the question , I must
lie between the roots . Hence,
` f(1) gt 0 `
`rArr 4p - p^(2) - 5 - 2p + 1 3p gt 0 ` lt brgt `rArr - p^(2) + 5p - 4 gt 0 `
`rArr p^(2) - 5p + 4 lt 0 `
`rArr (p - 4) (p - 1) lt 0 `
`rArr 1 lt p lt 4`
`rArr p in { 2, 3}`