Question

Solve the following quadratic equation by factorization, the absolute difference of roots are :
$(x-4)(x+2)=0$

Answer 1

$\Rightarrow$ $(x-4)(x+2)=0$

$\Rightarrow$ $x(x+2)-4(x+2)=0$

$\Rightarrow$ $x^2+2x-4x-8=0$

$\Rightarrow$ $x^2-2x-8=0$

$\Rightarrow$ $x^2-4x+2x-8=0$

$\Rightarrow$ $x(x-4)+2(x-4)=0$

$\Rightarrow$ $(x-4)(x+2)=0$

$\therefore$ $x=4,-2$

$\Rightarrow$ The difference between roots $=4-(-2)=4+2=6$