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In the real domain, yes. In the complex domain, no.

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โˆ™ 2009-10-14 10:10:35
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A polynomial of degree zero is a constant term

The grouping method of factoring can still be used when only some of the terms share a common factor A True B False

The sum or difference of p and q is the of the x-term in the trinomial

A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Q: Is it possible that the polynomial function doesn't have zeros?
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What is a quadratic polynomial which has no zeros?

A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.


What are the zeros of polynomials?

The values of the variables which make the polynomial equal to zero


How do you graph a polynomial in order to solve for the Zeros?

Either graph the polynomial on graph paper manually or on a graphing calculator. If it is a "y=" polynomial, then the zeroes are the points or point where the polynomial touches the x-axis. If it is an "x=" polynomial, then the zeroes are the points or point where the polynomial touches the y-axis. If it touches neither, then it has no zeroes.


How do you find the zeros of cubic polynomial equation?

If the cubic polynomial you are given does not have an obvious factorization, then you must use synthetic division. I'm sure wikipedia can tell you all about that.


How do you determine the zeros of a polynomial function?

In the general case, this is quite tricky. In high school, you learn some simple cases. If the polynomial is of degree 2, you can use the quadratic function. For higher degrees, in some specific cases you can use the methods taught in high school to factor the polynomial. As you might know, once the polynomial is completely factored, it is quite trivial to find the zeros. But in the general case, you need some iterative method, which is more appropriate for a computer. From Wikipedia, article "Polynomial": "Numerical approximations of roots of polynomial equations in one unknown is easily done on a computer by the Jenkins-Traub method, Laguerre's method, Durand-Kerner method or by some other root-finding algorithm." You can read about any of these methods for more information; but don't expect a formula where you just "plug in some numbers"; rather, those are iterative methods, that is, you need to repeat a certain calculation over and over until you get a root of a polynomial with the desired accuracy.

Related questions

What do the zeros of a polynomial function represent on a graph?

The zeros of a polynomial represent the points at which the graph crosses (or touches) the x-axis.


what are all of the zeros of this polynomial function f(a)=a^4-81?

Find All Possible Roots/Zeros Using the Rational Roots Test f(x)=x^4-81 ... If a polynomial function has integer coefficients, then every rational zero will ...


What are the zeros of a polynomial function?

the zeros of a function is/are the values of the variables in the function that makes/make the function zero. for example: In f(x) = x2 -7x + 10, the zeros of the function are 2 and 5 because these will make the function zero.


How do you find the zeros of any given polynomial function?

by synthetic division and quadratic equation


Can a polynomial have more zeros than the highest degree of the function?

no a plynomial can not have more zeros than the highest (degree) number of the function at leas that is what i was taught. double check the math.


What is a quadratic polynomial which has no zeros?

A quadratic polynomial must have zeros, though they may be complex numbers.A quadratic polynomial with no real zeros is one whose discriminant b2-4ac is negative. Such a polynomial has no special name.


What are the factors of a polynomial function with zeros at -2 and 7?

Since there are two zeros, we have: y = (x - (-2))(x - 7) y = (x + 2)(x - 7)


Why might it be useful to know the linear factors of a polynomial function?

It is useful to know the linear factors of a polynomial because they give you the zeros of the polynomial. If (x-c) is one of the linear factors of a polynomial, then p(c)=0. Here the notation p(x) is used to denoted a polynomial function at p(c) means the value of that function when evaluated at c. Conversely, if d is a zero of the polynomial, then (x-d) is a factor.


When the zeros of a polynomial function are 1 divided by2 and negative 1 what is the function?

Any multiple of X^2+X/2-1/2


What is a zero of a polynomial function?

A zero of a polynomial function - or of any function, for that matter - is a value of the independent variable (often called "x") for which the function evaluates to zero. In other words, a solution to the equation P(x) = 0. For example, if your polynomial is x2 - x, the corresponding equation is x2 - x = 0. Solutions to this equation - and thus, zeros to the polynomial - are x = 0, and x = 1.


What is a cubic polynomial function in standard form with zeros -4-5 and 5?

x3 + 4x2 - 25x - 100 = 0


Is it possible for a polynomial function of degree 3 to have no real zeros?

Yes - but only if the domain is restricted. Normally the domain is the whole of the real numbers and over that domain it must have at least one real zero.

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