If (x + a) is a factor of x2+px+q and x2+mx+n,then the value of a is
A
m−pn−q
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B
m+pn+q
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C
n−qm−p
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D
n+qm+p
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Solution
The correct option is Cn−qm−p Let f(x) = x2+px+q And q(x) = x2+mx+n (x + a) is a factor of f(x) and g(x) By remainder theorem, f(−a)=(−a)2+p(−a)+q=0 ⇒a2−ap+q=0 ...(i) Also, g(−a)=(−a)2+m(−a)+n=0 ⇒a2−am+n=0 ...(ii) Subtracting (ii) from (i) -a( p - m) + q - n = 0 ⇒−a(p−m)=−(q−n)⇒a(p−m)=q−n⇒a=n−qm−p