The lines `x+y-1=0,(m-1)x+(m^2-7)y-5=0,` and `(m-2)x+(2m-5)y=0` are a.) concurrent for three values of `m` b.) concurrent for no value of `m` c.) parallel for one value of `m` d.) parallel for two value of `m`

Options

A. concurrent for three values of m
B. concurrent for one value of m
C. concurrent for no value of m
D. parallel for m-3

Answer

C, D

Explanation

If the lines x+y-1 =0, (m-1)x +`(m^(2)-7)y-5 =0`, and (m-2) x+(2m-5)y = 0 are concurrent, then
`Delta = 0`
`"or " |{:(1,1,-1),(m-1, m^(2)-7, -5),(m-2, 2m-5, 0):}| = 0`
`"or " (m-2)(-5+m^(2)-7)-(2m-5)(-5+m-1)+0=0`
`"or " (m-2)(m^(2)-12)-(2m-5)(m-6)=0`
`"or " m^(3)-4m^(2)+5m-6=0`
`"or "(m-3)(m^(2)-m+2) = 0`
`"or "m = 3`
If m=3, then the two lines are parallel.