Q. 54.4( 9 Votes )

If the polynomial az3 + 4z3 + 3z – 4 and z3 – 4z + a leaves the same remainder when divided z – 3. Find a.

Answer :

z – 3 = 0

z = 3


Put value of z in both the equations.


az3 + 4z3 + 3z – 4


a(3)3 + 4(3)3 + 3(3) – 4


27a + 36 + 9 – 4


27a + 41 …… (1)


z3 – 4z + a


(3)3 – 4(3) + a


27 – 12 + a


15 + a …… (2)


Equate (1) and (2) as it is given that both the equations leave the same remainder


15 + a = 27a + 41


27a – a = 15 – 41


26a = –26


a = –1


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