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Question

If the polynomials az3+4z2+3z4 and z34z+a leave the same remainder when divided by z3, then find the value of a.
  1. 1
  2. 0
  3. 3
  4. 1

A
1
B
1
C
0
D
3
Solution
Verified by Toppr

Here, p(z)=a(z)3+4(z)2+3z4, q(z)=(z)34z+a, and the zero of z3 is 3.
So, by the given condition
p(3)=q(3)
a(3)3+4(3)2+3(3)4=(3)34(3)+a
27a+4×9+94=2712+a
27a+36+94=2712+a
27a+454=15+a
27a+41=15+a
27aa=1541
26a=26
a=2626
a=1

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