Question

EXERCISE 4.1
1. Check whether the following are quadratic equations :
(i) x² – 2x =(-2)(3 – x)
(ii) (x-2)(x+1)=(x - 1)(x+3)
(iii) (x − 3)(2x+1)= x(x + 5)​

Answer 1

Answer:

${x}^{2} - 2x = - 2(3 - x) \\ {x}^{2} - 2x = - 6 + 2x \\ {x}^{2} - 2x - 2x + 6 = 0 \\ {x}^{2} - 4x + 6 = 0 \\ its \: \: a \: quadratic \: equation.$

$(x - 2)(x + 1) = (x - 1)(x + 3) \\ {x}^{2} + x - 2x - 2 = {x}^{2} + 3x - x - 3 \\ {x}^{2} - x - 2 = {x}^{2} + 2x - 3 \\ {x}^{2} - {x}^{2} - x - 2x - 2 + 3 = 0 \\ - 3x + 1 = 0$

$(x - 3)(2x + 1) = x(x + 5) \\ 2 {x}^{2} + x - 6x - 3 = {x}^{2} + 5x \\ 2 {x}^{2} - 5x - 3 - {x}^{2} - 5x = 0 \\ {x}^{2} - 10x - 3 = 0 \\ its \: a \: qudratic \: equation.$