Q33 of 39 Page 91

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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