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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.
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
What is rational algebra expression?
Basically, a rational expression is one that can be written as one polynomial, divided by another polynomial.
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
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 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 ...
Is it possible that the polynomial function doesn't have zeros?
In the real domain, yes. In the complex domain, no.
How do you write a polynomial function with rational coefficients in standard form with given zeros of -1 -1 1?
The polynomial is (x + 1)*(x + 1)*(x - 1) = x3 + x2 - x - 1
How is a rational function the ratio of two polynomial functions?
That's the definition of a "rational function". You simply divide a polynomial by another polynomial. The result is called a "rational function".
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.
How do you figure out how many real zeros a problem has?
To find the number of real zeros of a function, you can use the Intermediate Value Theorem and graphing techniques to approximate the number of times the function crosses the x-axis. Additionally, you can apply Descartes' Rule of Signs or the Rational Root Theorem to analyze the possible real zeros based on the coefficients of the polynomial function.
The root of transcedence?
in math, a real number that is not the root of any polynomial with rational coefficients is called transcendental.
Which polynomial has rational coefficients a leading leading coefficient of 1 and the zeros at 2-3i and 4?
There cannot be such a polynomial. If a polynomial has rational coefficients, then any complex roots must come in conjugate pairs. In this case the conjugate for 2-3i is not a root. Consequently, either (a) the function is not a polynomial, or (b) it does not have rational coefficients, or (c) 2 - 3i is not a root (nor any other complex number), or (d) there are other roots that have not been mentioned. In the last case, the polynomial could have any number of additional (unlisted) roots and is therefore indeterminate.
How does my knowledge of polynomial function prepare me to understand rational function?
A rational function is the quotient of two polynomial functions.
What is rational algebra expression?
Basically, a rational expression is one that can be written as one polynomial, divided by another polynomial.
What about rational functions creates undefined and asymptotic behavior?
A rational function is the ratio of two polynomial functions. The function that is the denominator will have roots (or zeros) in the complex field and may have real roots. If it has real roots, then evaluating the rational function at such points will require division by zero. This is not defined. Since polynomials are continuous functions, their value will be close to zero near their roots. So, near a zero, the rational function will entail division by a very small quantity and this will result in the asymptotic behaviour.
