Question

 If a specific number x = a is substituted for the variable x in a polynomial, so that the value is zero, then x = a is said to be​

Answer 1

Answer:

a” would be considered a “zero” of the polynomial function since its value would produce a value of 0 for the polynomial function. Another term that is used is “root”. “a” would be a “root” of the polynomial equation when it is equated to 0. Another term that is used is “x-intercept”. “a” would be an “x-intercept” of the graph of the function since the value of “a” would occur at the point where the graph of the function intersects the x-axis.

Step-by-step explanation:

Answer 2

Step-by-step explanation:

The fundamental theorem of algebra states that every non-constant, single- variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with zero as its coefficient.

The fundamental theorem is also stated as follows: every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. The equivalence of the two statements can be proven through the use of successive polynomial division.

Key Terms

multiplicity: the number of values for which a given condition holds

Some polynomials with real coefficients, like x2+1, have no real zeros. As it turns out, every polynomial with a complex coefficient has a complex zero. Every polynomial of odd degree with real coefficients has a real zero.

The Fundamental Theorem

The fundamental theorem of algebra says that every non-constant polynomial in a single variable z, so any polynomial of the form

cnxn+cn−1xn−1+…c0

where n>0 and cn≠0, has at least one complex root.