# If (x + a) is a factor of two polynomials x2 + px + q and x2 + mx + n then prove that : As, (x – a) is a factor.

So, x = – a must satisfy the given equations.

( – a)2 + p.( – a) + q = 0

a2 – ap + q = 0 ...... (i)

Also, ( – a)2 + m.( – a) + n = 0

a2 – am + n = 0 ...... (ii)

Equating (i)& (ii):

a2 – ap + q = a2 – am + n

– ap + q + – am + n

am – ap = n – q

a(m – p) = n – q Hence, Proved.

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