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State whether the following statement is true or false.

The zero of a polynomial must always be 0.

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True

False

answer is B.

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Detailed Solution

Given, the zero of a polynomial must always be 0.
The zero of any polynomial is a real number that satisfies the given polynomial.
If

x = k

is a zero of the polynomial

p (x),

then we must have

p (k) = 0.

Let’s suppose

p (x) = x − 2 .

Then

x = 2

is a zero of the polynomial

p (x) = x − 2

p (2) = 0.

Since, the zero of the polynomial

p (x) = x − 2

is equal to 2, which is not 0.
Therefore the zero of a polynomial could be any number.
Thus, the given statement is not true.
Hence, option (2) is correct.

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