Question

For how many real values of ${}^{\prime }{m}^{\prime }$ the points $A(m+1,1),B(2m+1,3)$ and $C(2m+2,2m)$ are collinear.

Answer 1

The points will be collinear if

$\frac{3-1}{2m+1-m-1}=\frac{2m-3}{2m+2-2m-1}$

$\frac{2}{m}=\frac{2m-3}{1}$

$2=2m^2-3m$

$2m^2-3m-2=0$

$mhastwopossitiverealroots$