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Question

If x+a is a common factor of expressions f(x)=x2+px+q and g(x)=x2+mx+n, then 'a' is equal to:

A
nqmp
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B
n+qm+p
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C
nm
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D
mn
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Solution

The correct option is A nqmp
Given:
x+a is a factor of polynomialsf(x)=x2+px+q and g(x)=x2+mx+n

Using factor theorem,
f(a)=0
a2ap+q=0(i)

Again using factor theorem,
g(a)=0
g(a)=a2am+n(ii)

Equating (i) and (ii), we get:
a2ap+q=a2am+n
amap=nq
a(mp)=nq
a=nqmp

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