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Question

A polynomial whose degree is not defined is .

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Solution

Zero Polynomial:––––––––––––––––––––
We learnt earlier that f(x)=anxn+an1xn1++a1x+a0f(x)=anxn+an1xn1++a1x+a0 is a polynomial.
Now, a zero polynomial is a special case of the polynomial where all the coefficients an,an1,an2,a1,a0 are zeros (0). Hence, the polynomial becomes f(x)=0 or the corresponding polynomial function is the constant function with value 0.
f(x)=0, g(x)=0x, h(x)=0x2,p(x)=0x3, q(x)=0x12, r(x)=0x50
etc. are all examples of zero polynomials.
As seen in the examples above, the degree of a zero polynomial can be 0, 1, 2, 3, 12, 50, and so on, indicating that the degree of a zero polynomial is not a fixed number. As a result, the degree of a zero polynomial isn't defined.

Note:–––––
The zero polynomial is considered as the additive identity of the polynomials.

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