Question

Solve by factorization method:
$6x^2+(a-11)x-(a^2+3a-4)=0$

• A. (a-1)/2 and (a+4)/3
• B. (-a-1)/2 and (a-4)/3
• C. (-a+1)/2 and (a+4)/3
• D. (a-1)/2 and (-a+4)/3

Answer 1

The correct option is C (-a+1)/2 and (a+4)/3

$6x^2+(a-11)x-(a^2+3a-4)=0$
$\Rightarrow 6x^2+\left(\right(3a-3)-(2a+8\left)\right)x-(a+4)(a-1)=0$
$\Rightarrow 6x^2+(3a-3)x-(2a+8)x-(a+4)(a-1)=0$
$\Rightarrow 3x[2x+(a-1\left)\right]-(a+4)[2x+(a-1\left)\right]=0$
$\Rightarrow [2x+(a-1\left)\right][3x-(a+4\left)\right]=0$
$\Rightarrow 2x+(a-1)=0or3x-(a+4)=0$
$\Rightarrow 2x=-a+1$ or $3x=a+4$
$\Rightarrow x=\frac{1-a}{2}$ or $x=\frac{a+4}{3}$

So, option c is correct.