Question

factorise 12x^2-x-6​

Answer 1

Answer:

Step-by-step explanation:

$12x^2-x-6$

using the quadratic formula : D=b^2-4ac

a=12

b= -1

c = -6

applying the formula : (-1)^2 - 4(12)(-6) = 289

then for finding the roots of equation : {-b+ D^(1/2) } / 2a ,  {-b-D^(1/2) / 2a}

that gives,                                                 $\sqrt{D} = 17, D^{2}= 289$

$(-b + \sqrt{D} )/2a$

and $(-b -\sqrt{D} ) / 2a$

solving the above equations , we get  

ANS :

18/24   and -16/ 24

Answer 2

$12x^{2}-x - 6 \\ = 12 {x}^{2}-9x+8x - 6 \\ = 3x(4x - 3) + 2(4x - 3) \\ = (3x + 2)(4x - 3) \\ \\ (3x + 2) = 0 \: \: \: \: or \: (4x - 3) = 0 \\ 3x = - 2 \: \: \: \: \: \: \: \: \: \: \: or \: \: 4x = 3 \ \\ x = \frac{ - 2}{3} \: \: \: \: \: \: \: \: \: \: \: or \: \: x = \frac{3}{4} \\ so \: \: \: the \: \ \: factors \: \: are \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = \frac{ - 2}{3} \: and \: \frac{3}{4}$

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