Question

Solve the following quadratic equation using the quadratic formula :
abx²+(b²-ac)x-bc=0

Answer 1

Here, a=ab

b= b2-4ac

c= -bc

Now, b2-4ac

= (b2-ac)2-4.ab.(-bc)

= b4+a2c2-2b2ac+4b2ac

= b4+a2c2+2b2ac

= (b2+ac)2

Now, √b2-4ac= b2+ac

Putting it in quadratic formula,

x=(-b ± √b2-4ac)/2a

=> x=(-b2+ac±b2+ac)/2ab

=> x=-b2+ac+b2+ac/2ab or -b2+ac-b2+ac/2ab

=> x= 2ac/2ab or -2b2+2ac/2ab

=> x= c/b or x= 2(-b2+ac)/2ab or x= ac-b2/ab

Hope it helps!