The maximum number of turning points is 5 – 1 = 4.

The zeros of a function f are found by solving the equation f(x) = 0.

So if is a zero, then is also a zero. There are 11 zeros in a degree 11 polynomial function. Since, given the fact that you have at least 4 complex zeros, the maximum number of real zeros must be 11 minus 4. Since you are given that there is one real zero the maximum number of complex zeros is 11 minus 1.

Possible number of positive real zeros: Since we have 3 sign changes with f(x), then there is a possibility of 3 or 3 – 2 = 1 positive real zeros.

We generally want the quadratic to equal zero, however, because the solutions are the roots of the quadratic. Roots of functions, i.e. the solutions(s) of functions the form f(x)=0 are very important.

In the same way, the x-axis is also the line “y = 0”. Then, algebraically, an x-intercept is a point on the graph where y is zero, and. a y-intercept is a point on the graph where x is zero.

They get this name because they are the values that make the function equal to zero. Zeros of functions are extremely important in studying and analyzing functions. In fact, they’re so important and hold so many different properties and explanations that we have two other names for them as well.

The sine function has no algebraic zeros except 0, but has infinitely many transcendental zeros: −3π, −2π, −π, π, 2π, 3π,. . .

In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function , is a member of the domain of such that vanishes at ; that is, the function attains the value of 0 at , or equivalently, is the solution to the equation. .

THE ROOTS, OR ZEROS, OF A POLYNOMIAL. It is a solution to the polynomial equation, P(x) = 0. It is that value of x that makes the polynomial equal to 0.

Roots are also called x-intercepts or zeros. The roots of a function are the x-intercepts. By definition, the y-coordinate of points lying on the x-axis is zero. Therefore, to find the roots of a quadratic function, we set f (x) = 0, and solve the equation, ax2 + bx + c = 0.

1 Answer. The zeros of a function represent the x value(s) that result in the y value being 0. The zeros of a function represent the root(s) of a function. The zeros of a function represent the solution(s) of a function.

The number of times a given factor appears in the factored form of the equation of a polynomial is called the multiplicity. The zero associated with this factor, x=2 , has multiplicity 2 because the factor (x−2) occurs twice. We call this a triple zero, or a zero with multiplicity 3.

Multiplicity most commonly means a large number or a great variety. It is the noun form of the adjective multiple, meaning more than one or several. It can also mean the state of being multiple.