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Question

If a polynomial az3+4z2+2z−4 and z2+4z+a leave the same remainder divide by (z−3). Find the value of a.

A
1
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B
1726
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C
1
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D
17
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Solution

The correct option is C 1726
Let f(z)=az3+4z2+2z4

It is given that the zero of the polynomial f(z) is (z3) that is z=3

So,replacing z by 3, we get

f(3)=a(3)3+4(3)2+2(3)4=27a+(4×9)+64=27a+36+64=27a+424=27a+38

Let g(z)=z2+4z+a

It is given that the zero of the polynomial f(z) is (z3) that is z=3

So,replacing z by 3, we get

g(3)=(3)2+(4×3)+a=9+12+a=21+a

Now, since the given two polynomials leaves same remainder when divided by z3.
Therefore, g(3)=f(3) that is:

27a+38=21+a27aa=213826a=17a=1726

Hence, a=1726.

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