Question

if x²-x-6 and x²+3x-18 have a common factor (x-a) then find the 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

Answer:

a= -6

Explanation:

let p(x)=x²-x-6

and f(x)=x²+3x-18

Now, (x-a) is factor of both

x-a=0

x=a

put x=a in p(x)

we get, p(a)=a²-a-6 = 0

a²-a = 6...........1.

now put x=a in f(x)

we get,f(a)=a²-3a-18 = 0

a²-3a = 18

a²= 18+3a

put in 1.

we get, 18+3a-a = 6

2a = 6-18

2a = -12

a = -12/2

a = -6