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Question

The number of the distinct zeroes of the polynomial f(x)=x(x4)3(x3)2(x1) is

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Solution

Given polynomial f(x)=x(x4)3(x3)2(x1)
For zeroes of a polynomial
f(x)=0x(x4)3(x3)2(x1)=0x=0,(x4)3=0,(x3)2=0,(x1)=0x=0,4,4,4,3,3,1
The distinct zeroes of the polynomial are x=0,1,3,4
Hence, the number of distinct zeroes of the polynomial is 4.

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