Question

X2-x-6 and x2+3x-18 have common factor x-a find value of a

Answer 1

x2-x-6=0
x2-3x+2x-6=0
x(x-3)+2(x-3)=0
(x-3)(x+2)=0

x2+3x-18=0
x2+6x-3x-18=0
x(x+6)-3(x+6)=0
(x+6)(x-3)=0

therfore x-3 is common in both equations therefore a=3

Answer 2

since x-a is the common factor therefore x=a is the common zero of both the equations..
therefore x=a will satisfy both the equation...
a^2-a-6=0 and a^2+3a-18=0
a^2-3a+2a-6=0 and a^2+6a-3a-18=0
(a-3)(a+2)=0 and (a+6)(a-3)=0
a=3 or a= -2 and a= -6 or a=3

therefore a is the common root this means value of a is 3

hope this helps u..