If x1,y1  are roots of x2+8x−20=0 ,x2,y2  are the roots  of 4x2+32x−57=0  and (x3,y3) are the roots of 9x2+72x−112=0 , then the points (x1,y1) ,(x2,y2)  and (x3,y3)

x1+y1=−8,x2+y2=−324=−8,x3+y3=−729=−8 ∴ the determinant  =|1x1y11x2y21x3y3|=|1x1+y1y11x2+y2y21x3+y3y3|=|1−8y11−8y21−8y3|=0 [first and second columns are proportional]Hence, the points (x1,y1),(x2,y2) and (x3,y3)  are collinear.