Q. 334.7( 7 Votes )

# If (x + a) is a factor of two polynomials x^{2} + px + q and x^{2} + mx + n then prove that :

Answer :

As, (x – a) is a factor.

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

⇒ ( – a)^{2} + p.( – a) + q = 0

⇒ a^{2} – ap + q = 0 ...... (i)

Also, ( – a)^{2} + m.( – a) + n = 0

⇒ a^{2} – am + n = 0 ...... (ii)

Equating (i)& (ii):

⇒ a^{2} – ap + q = a^{2} – am + n

⇒ – ap + q + – am + n

⇒ am – ap = n – q

a(m – p) = n – q

Hence, Proved.

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