The prime polynomial function is . Option C is correct.
Further explanation:
The Fundamental Theorem of Algebra states that the polynomial has roots if the degree of the polynomial is n.
The polynomial function has n roots or zeroes.
Given:
The options are as follows,
(a).
(b).
(c).
(d).
Explanation:
From the graph of option (a) it has been observed that the polynomial has one root at . Therefore, it is not a prime polynomial function.
From the graph of option (b) it has been observed that the polynomial has two roots at and . Therefore, it is not a prime polynomial function.
From the graph of option (c) it has been observed that the polynomial has no root. Therefore, it is a prime polynomial function.
From the graph of option (d) it has been observed that the polynomial has two roots. Therefore, it is not a prime polynomial function.
The prime polynomial function is . Option C is correct.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Polynomial
Keywords: roots, prime polynomial, linear equation, quadratic equation, zeros, function, polynomial, solution, cubic function, degree of the function.