Question

Read the statements given for the degree and zeroes of a polynomial p(x) = axb + c (for a, b > 1) and choose the correct option. Statement I: Degree of the polynomial can be greater or smaller than number of zeroes. It depends upon the polynomial. Statement II: Number of zeroes of p(x) will always be less than or equal to b. (A) Only I is Correct (C) Both I and II are Correct (B) Only II is Correct (D) Both I and II are Incorrect​

Answer 1

Given :  polynomial p(x) = axᵇ + c (for a, b > 1)

Statement I: Degree of the polynomial can be greater or smaller than number of zeroes. It depends upon the polynomial.

Statement II: Number of zeroes of p(x) will always be less than or equal to b

To Find : Correct option :

(A) Only I is Correct

(B) Only II is Correct

(C) Both I and II are Correct

(D) Both I and II are Incorrect​

Solution:

polynomial p(x) = axᵇ + c (for a, b > 1)

Hence degree of polynomial is b

Number of Zeroes  of  polynomial  with degree b  will always be  less than or equal to b

Hence  Statement II: is correct

Statement I: Degree of the polynomial can be greater or smaller than number of zeroes. It depends upon the polynomial.  INCORRECT

as Degree of the polynomial  can not be smaller than number of Zeroes

Hence only Statement II  is CORRECT

(B) Only II is Correct

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