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Question

If x+a is a common factor of f(x)=x2+x−6 and g(x)=x2+3x−18 then find the value of a.

A
1
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B
2
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C
3
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D
No value of a exist
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Solution

The correct option is B No value of a exist
Given that:
f(x)=x2+x6 and g(x)=x2+3x18
Since x+a is common factor of f(x)&g(x) than f(a)&g(a) will be zero.
So,

f(a)=(a)2+(a)6=0f(a)=a2a6=0

So, a2a6=0a23a+2a6=0

a(a3)+2(a3)=0

(a+2)(a3)=0

So a=3,2........(1)

Since

g(a)=(a)2+3(a)18=0a23a18=0

a26a+3a18=0

a(a6)+3(a6)=0

(a6)(a+3)=0

a=6,3.........(2)

compering equation 1 and 2.

a has no solution.

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