Question

Check whether the following are quadratic equations:
1)(x-2)(x+1)=(x-1)(x+3)
2) (x²+3x+1)=(x-2)²
3) (x+2)³=2x(x²-1)
4)x³-4x²-x+1=(x-2)³

Answer 1

1) (x-2) (x+1)=(x-1) (x+3)
on multiple
x²+x-2x-2=x²+3x-x-3
x²-x-2=x²+2x-3
(x² get cancelled and taking at L. H. S)
-x-2x-2-3=0
-3x-5=0
hence it is quadratic equation because as we it is not in the form of ax²+bx+c=0,where b≠0
hence here is b≠0 so it is quadratic equation