Question

1. Check whether the following are quadratic equations :
(ii) x2 - 2x =(-2) (3 - x)
(1) (x + 1)2 = 2(x-3)
(iv) (x-3)(2x +1)= x(x+5)
(ii) (x-2)(x+1)=(x - 1)(x + 3)
(vi) x + 3x+1=(x - 2)
(v) (2x - 1)(x-3) = (x + 5)(x - 1)
(viii) x - 4x2 - x + 1 = (x - 2)
(vii) (x + 2) = 2x (x - 1)

Answer 1

Step-by-step explanation:

Check whether the following are quadratic equations :

$(1){x}^{2} - 2x = - 2(3 - x) \\ \\ {x}^{2} - 2x = - 6 + 2x \\ \\ {x}^{2} - 4x + 6 = 0 \\ \\ Yes,\: it \: is \: a \: quadratic \: equation$

$(2) {(x + 1)}^{2} = 2(x - 3) \\ \\ {x}^{2} + 2x + 1 = 2x - 6 \\ \\ {x}^{2} + 7 = 0 \\\\ Yes, \: it \: is \: a \: quadratic \: equation$

$(3) (x-3)(2x +1)= x(x+5) \\ \\ 2 {x}^{2} + x - 6x - 3 = {x}^{2} + 5x \\ \\ {x}^{2} - 10x - 3 = 0 \\ \\ Yes ,\: it \: is \: a \: quadratic \: equation$

$(4) (x-2)(x+1)=(x - 1)(x + 3) \\ \\ {x}^{2} + x - 2x - 2 = {x}^{2} + 3x - x - 3 \\ \\ - x - 2 = 2x - 3 \\ \\ - 3x + 1 = 0 \\ \\ No, \: it \: is \: not \: a \: quadratic \: equation$

$(5) x + 3x+1=(x - 2) \\ \\ x + 3x + 1 = x - 2 \\ \\ 3x + 3 = 0 \\ \\ No, \: it \: is \: not \: a \: quadratic \: equation$

$(6) (2x - 1)(x-3) = (x + 5)(x - 1) \\ \\ 2 {x}^{2} - 6x - x + 3 = {x}^{2} - x + 5x - 5 \\ \\ {x}^{2} - 11x + 8 = 0 \\ \\ Yes, \: it \: is \: a \: quadratic \: equation$

$(7)x - 4 {x}^{2} - x + 1 = (x - 2) \\ \\ - 4 {x}^{2} + 1 - x + 2 = 0 \\ \\ - 4 {x}^{2} - x + 3 = 0 \\ \\ Yes, \: it \: is \: a \: quadratic \: equation$

$(8) (x + 2) = 2x (x - 1) \\ \\ x + 2 = 2 {x}^{2} - 2x \\ \\ - 2 {x}^{2} + 3x + 2 = 0 \\ \\ Yes, \: it \: is \: a \: quadratic \: equation$

Hope it helps you.

Answer 2

Answer:

Step-by-step explanation:

HLO