Q. 54.4( 9 Votes )

# If the polynomial az^{3} + 4z^{3} + 3z – 4 and z^{3} – 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.

az^{3} + 4z^{3} + 3z – 4

a(3)^{3} + 4(3)^{3} + 3(3) – 4

27a + 36 + 9 – 4

27a + 41 …… (1)

z^{3} – 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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