Factorise : $12 x^{2}-7 x+1$
Factorise : $12 x^{2}-7 x+1$
$12 x^{2}-7 x+1$
Here co-efficient of $\quad x^{2}=12$
Co-efficient of $x=-7$
and constant term $=1$ $\therefore $ $a =12, \,b =-\,7, \,c =1$
Now, $l+ m =-7$ and $lm = ac =12 \times 1$
$\therefore$ we have $l=(-4)$ and $m =(-3)$ i.e. $b =-7=(-4-3)$
Now, $12 x^{2}-7 x+1=12 x^{2}-4 x-3 x+1$
$=4 x(3 x-1)-1(3 x-1)=(3 x-1)(4 x-1)$
Thus, $12 x^{2}-7 x+1=(3 x-1)(4 x-1)$
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