Question

1.check whether the following are Quadratic equations:
(v) (2x - 1)(x-3) = (x + 5)(x - 1)
(vii) (x + 2) = 2x (x² - 1)
(vi) x² + 3x + 1 = (x - 2)2
(viii) x2 - 4x - x + 1 = (x - 2)​

Answer 1

Answer:

1. $(2x - 1)(x - 3) = (x + 5)(x - 1) \\ 2 {x}^{2} - 6x - x + 3 = {x}^{2} - x + 5x - 5 \\ 2 {x}^{2} - 7x + 3 = {x}^{2} + 4x - 5 \\ {x}^{2} - 11x + 8 = 0 \\ its \: a \: quadratic \: equation.$
2. $(x + 2) = 2x( {x}^{2} - 1) \\ x + 2 = 2 {x}^{3} - 2x \\ 2 {x}^{3} - 3x - 2 = 0 \\ it \: is \: not \: a \: quadratic \: equation.$
3. ${x}^{2} + 3x + 1 = (x - 2) ^{2} \\ {x}^{2} + 3x + 1 = {x}^{2} + 4 - 4x \\ 7x - 3 = 0 \\ it \: is \: not \: a \: quadratic \: equation.$
4. ${x}^{2} - 4x - x + 1 = (x - 2) \\ {x}^{2} - 5x + 1 = x - 2 \\ {x}^{2} - 6x + 3 = 0 \\ its \: a \: quadratic \: equation.$