Total Questions :29

(i) (x + 2)2 = 2(x - 3)
⇒ x2 + 2x + 1 = 2x - 6
⇒ x2 + 7 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.

(ii) x2 - 2x = (-2)(3 - x)
⇒ x- 2x = -6 + 2
⇒ x- 4x + 6 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.

(iii) (x - 2)(x + 1) = (x - 1)(x + 3)
⇒ xx - 2 = x+ 2x - 3
⇒ 3x - 1 =0
It is not of the form ax2 + bx + c = 0.
Hence, the given equation is not a quadratic equation.

(iv) (x - 3)(2x + 1) = x(x + 5)
⇒ 2x- 5x - 3 = x+ 5x
⇒  x- 10x - 3 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.

(v) (2x - 1)(x - 3) = (x + 5)(x - 1)
⇒ 2x- 7x + 3 = x+ 4- 5
⇒ x- 11x + 8 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is 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)
⇒ x3 + 8 + x2 + 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 - 4x2 - x + 1 = (x - 2)3
⇒  x3 - 4x2 - x + 1 = x3 - 8 - 6x + 12x
⇒ 2x2 - 13x + 9 = 0
It is of the form ax2 + bx + c = 0.
Hence, the given equation is quadratic equation.