Question

1Q)Factories the following:-

1)6x^2-x-2=0
2)3x^2-2✓6+2=0
3)2x^2+x-300=0
4)2x^2-5x+3=0.....

Please answer it neatly, with step by step.​

Answer 1

Answer:

$6{x}^{2} -x - 2 = 0 \\ 6 {x}^{2} - 4x + 3x - 2 = 0\\ 2x(3x - 2) + 1(3x - 2) = 0\\ (2x + 1)(3x - 2) = 0 \\ 2x + 1 = 0 \: \: \: \: \: \: \: \: 3x - 2 = 0\\ x = - \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{2}{3}$

$3 {x}^{2} - 2 \sqrt{6} + 2 = 0$

$3 {x}^{2} = 2 \sqrt{6} - 2$

${x}^{2} = \frac{2 \sqrt{6} - 2 }{3}$

$x = \sqrt{ \frac{2 \sqrt{6 } - 2 }{3} }$

$2 {x}^{2} + x - 300 = 0$

$2 {x}^{2} + 25x - 24x - 300 = 0$

$x(2x + 25) - 12(2x + 25) = 0$

$(x - 12)(2x + 25) = 0$

$x - 12 = 0 \: \: \: \: \: \: \: \: \: \: 2x + 25 = 0 \\ x = 12 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2x = - 25 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{ - 25}{2}$

4 is homework for you