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.


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