If (ax2+bx+c)y+a′x2+b′x+c′=0, then the condition that x may be rational function of y is
A
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is A The given equation can be written as (ay+a′)x2+(by+b′)x+(cy+c′)=0 The condition that x may be rational function of y is, (by+b′)2−4(ay+a′)(cy+c′) is a perfect square that is, (b2−4ac)y2+(2bb′−4ac′−4a′c)y+b′2−4a′c′ is a perfect square ⇒D=0 that is, 4(bb′−2ac′–2a′c)2−4(b2−4ac)(b′2−4a′c′)=0 or (ac′+a′c)−4aa′cc′=abb′c+a′bb′c–a′bb′c–a′c′b2−acb′2 or (ac′−a′c)2=(ab′−a′b)(bc′−b′c)