Question

Question 1 Check whether the following are quadratic equations:
(i) (x+1)^2 = 2(x-3)
(ii) x^2 - 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) x^2 + 3x + 1 = (x-2)^2
(vii) (x+2)^3 = 2x(x^2 - 1)
(viii) x^3 - 4x^2 - x + 1 = (x-2)^3

Class 10 - Math - Quadratic Equations Page 73

Answer 1

(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)
⇒ 2x2 - 5x - 3 = x2 + 5x
⇒  x2 - 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)
⇒ 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.

Answer 2

Answer:

hey mate here is ur answer