Check whether the following are quadratic equations :
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii)
(viii)
(i) (x+1)2 = 2(x-3)
x2+2x+1 = 2x-6
x2+7 = 0
Equation is in the form of ax2+bx+c = 0.
So, we can say that the given equation is a quadratic equation.
(ii) x2 – 2x = (-2)(3 – x )
x2 – 2x = -6 + 2x
x2 – 4x +6 = 0
Equation is in the form ax2+bx+c = 0.
Hence, the given equation is a quadratic equation.
(iii) (x – 2 )(x+1) = (x – 1 )(x+3)
x2 – x – 2 = x2+2x – 3
3x – 1 = 0
Equation is not in the form ax2+bx+c = 0.
Hence, the given equation is not a quadratic equation.
(iv) (x – 3 )(2x+1) = x(x+5)
2x2 – 5x – 3 = x2 +5x
x2 – 10x – 3 = 0
Equation is in the form ax2+bx+c = 0.
Hence, the given equation is a quadratic equation.
(v) (2x – 1 )(x – 3 ) = (x+5)(x – 1 )
2x2 – 7x + 3 = x2+4x – 5
x2 – 11x+8 = 0
Equation is in the form ax2+bx+c = 0.
Hence, the given equation is a quadratic equation.
(vi) x2+3x+1 = (x – 2 )2
x2+3x+1 = x2+4 – 4x
7x – 3 = 0
It is not of the form ax2+bx+c = 0.
Hence, the given equation is not a quadratic equation.
(vii) (x+2)3 = 2x (x2-1)
x4 + 8 + 6x2 +12x = 2x3 – 2x
x3 – 14x - 6x2 – 8 = 0
It is not of the form ax2+bx+c = 0.
Hence, the given equation is not a quadratic equation.
(viii) X3 – 4x3 – x +1 = (x-2)3
X3 – 4x2 –x +1 = x3 – 8 – 6x2 +12x
2x2 – 13x + 9 = 0
It is of the form ax2+bx+c = 0.
Hence, the given equation is a quadratic equation.