Answer:
C.{3, -2}
Step-by-step explanation:
Solving the quadratic equation by factorization:
[tex]x^{2} - x - 6 = 0[/tex]
we will find two factors that when multiplied together will give [tex]-6x^{2}[/tex] and when added together will give [tex]-x[/tex]
the factors are : [tex]-3x[/tex] and [tex]2x[/tex]
check :
[tex]-3x[/tex] x [tex]2x[/tex] = [tex]-6x^{2}[/tex]
[tex]-3x + 2x = -x[/tex]
we will substitute this values into the equation , that is
[tex]x^{2} - 3x + 2x - 6 = 0[/tex]
[tex](x^{2} -3x ) + (2x - 6 ) = 0[/tex]
factorizing , we have
[tex]x ( x - 3 ) + 2 ( x - 3 ) = 0[/tex]
factorizing [tex]x-3[/tex] out , we have
[tex]( x -3 ) ( x + 2 ) = 0[/tex]
either [tex]x - 3 = 0[/tex] or [tex]x + 2 = 0[/tex]
Therefore :
[tex]x = 3[/tex] or [tex]-2[/tex]
