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Answers
(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)
⇒x2 - 2x = -6 + 2x
x2 - 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)
⇒ x2-x - 2 = x2 + 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)
⇒ 2x25x3 = x2 + 5x
⇒ x2-10x3=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)
⇒ 2x2 - 7x + 3 = x2 + 4x - 5
x2 - 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=x3-8-6x2 + 12x
⇒ 2x2 13x +9=0
It is of the form ax2 + bx + c = 0. Hence, the given equation is quadratic equation.