Question

factorise 12x^2-10x+2

Answer 1

Step-by-step explanation:

We Have :-

$12x^{2} - 10x + 2$

To Find :-

$factors \: and \: zeroes$

Method Used :-

$middle \: term \: splitting$

Solution :-

$12x^{2} - 10x + 2 \\ \\ \\ 12x^{2} - 6x - 4x + 2 \\ \\ \\ 6x(2x - 1) - 2(2x - 1) \\ \\ \\ (2x - 1)(6x - 2) \\ \\ \\ 2x - 1 = 0 \\ \\ \\ 2x = 1 \\ \\ \\ x = \dfrac{1}{2} \\ \\ \\ 6x - 2 = 0 \\ \\ \\ 6x = 2 \\ \\ \\ x = \dfrac{1}{3}$

Answer 2

↪Question :-

• Factorise : $\sf{12x^2-10x+2}$

↪Solution:-

Given :

• $\sf{12x^2-10x+2}$

To Find :

• Factorise

We have to find two numbers whose sum is -10 and product is 24. So, the numbers are -6 and -4.

$\sf{: \implies{12x^2-10x+2}} \\ \\ \sf{: \implies{12x^2+( - 6 - 4) x+ 2}} \\ \\ \sf{: \implies{12x^2 - 6 x - 4x + 2}} \\ \\ \sf{: \implies{6x(2x - 1) -2( 2x - 1})} \\ \\ \sf{: \implies{(2x - 1)(6x - 2 )}}$

Now, we solve quadratic equation :

$\sf{ : \implies{(2x - 1)(6x - 2 ) = 0} } \\ \\ \sf{ : \implies{2x = 0 + 1 \: or \: 6x = 0 + 2}} \\ \\ \sf{ : \implies{2x = 1 \: or \: 6x = 2}} \\ \\ \sf{ : \implies{x = \dfrac{1}{2} \: or \: x = \dfrac{2}{6} }} \\ \\ \sf{ : \implies{x = \dfrac{1}{2}\: or \: x = \dfrac{1}{3} }}$

$\rule {307}{2}$