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

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Can a polynomial be no rational zeros but have real zeros?

Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.


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.


State whether the following is a polynomial function give the zero s of the function if the exist f x x 2-6x plus 8?

The function ( f(x) = x^2 - 6x + 8 ) is a polynomial function because it is a quadratic expression. To find the zeros, we can factor it as ( (x - 2)(x - 4) ), which gives us the zeros ( x = 2 ) and ( x = 4 ). Thus, the zeros of the function are 2 and 4.


What is a polynomial function f of least degree that has rational coefficient a leading coefficient of 1 and the given zeros -7 -4?

A polynomial function of least degree with rational coefficients and a leading coefficient of 1 that has the zeros -7 and -4 can be constructed using the fact that if ( r ) is a zero, then ( (x - r) ) is a factor. Therefore, the polynomial can be expressed as ( f(x) = (x + 7)(x + 4) ). Expanding this, we get ( f(x) = x^2 + 11x + 28 ). Thus, the polynomial function is ( f(x) = x^2 + 11x + 28 ).

Related Questions

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 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 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 be no rational zeros but have real zeros?

Yes, a polynomial can have no rational zeros while still having real zeros. This occurs, for example, in the case of a polynomial like (x^2 - 2), which has real zeros ((\sqrt{2}) and (-\sqrt{2})) but no rational zeros. According to the Rational Root Theorem, any rational root must be a factor of the constant term, and if none exist among the possible candidates, the polynomial can still have irrational real roots.


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.


State whether the following is a polynomial function give the zero s of the function if the exist f x x 2-6x plus 8?

The function ( f(x) = x^2 - 6x + 8 ) is a polynomial function because it is a quadratic expression. To find the zeros, we can factor it as ( (x - 2)(x - 4) ), which gives us the zeros ( x = 2 ) and ( x = 4 ). Thus, the zeros of the function are 2 and 4.


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.


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)


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 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.