The value of 'p' for which the equation `x^2+pxy+y^2-5x-7y+6=0` represents a pair of straight lines , is

Options

A. `5//2`
B. `5`
C. `2`
D. `2//5`

Answer

A

Explanation

Given equation , `x^2+pxy+y^2-5x-7y+6=0`
will represent a pair of straight lines , if
`.1.6+2(-(7)/(2))((-5)/(2))((p)/(2))-1((-7)/(2))^2-1((-5)/(2))^2-6((p)/(2))^2=0`
`rArr 6+(35P)/(4)-(49)/(4)-(25)/(4)-(6p^2)/(4)=0`
`rArr 35p-50-6p^2=0rArr 6p^2-35p+50=0`
`rArr (2p-5)(3p-10)=0`
`therefore p=(5)/(2),(10)/(3)`