Check whether the following are quadratic equations: (i) (x+1)²=2(x-3) (ii) x²-2x=(-2)(3-x) (iii) (x-2)(x+1)=(x-1)(x+3) (iv) (x-3)(2x+1)=x(x+5) (v) (2x-1)(x-3)=(x+5)(x-1) (vi) x²+3x+1=(x-2)² (vii) (x+2)³=2x(x²-1) (viii) x³-4x²-x+1=(x-2)³

Quadratic equation is a polynomial equation in which the degree is 2. General form of a Quadratic equation is ax²+bx+c=0, a≠0

i) (x+1)²=2(x-3)
x²+2x+1=2x-6
x²+7=0 →Quadratic

ii) x²-2x=(-2)(3-x)
x²-2x=-6+2x
x²+4x+6=0 →Quadratic

iii) (x-2)(x+1)=(x-1)(x+3)
x²-x-2=x²+2x-3
3x=1 →Non Quadratic

iv) (x-3)(2x+1)=x(x+5)
2x²-5x-3=x²+5x
x²+10x-3=0 →Quadratic

v) (x-3)(2x-1)=(x-1)(x+5)
2x²-7x+3=x²+4x-5
x²-11x+8=0 →Quadratic

vi) x²+3x+1=(x-2)²
x²+3x+1=x²-4x+4
7x=3 →Non Quadratic

vii) (x+2)³=2x(x²-1)
x³+8+6x(x+2)=2x³-2x
x³+8+6x²+12x=2x³-2x
-x³+6x²+14x+8=0 →Non Quadratic

viii) x³-4x²-x+1=(x-2)³
x³-4x²-x+1=x³-6x²+12x-8
2x²-13x+9=0 →Quadratic