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Why is roots of even or odd hurwitz polynomial found on the jw axis only?
Wiki User
∙ 13y ago
Actually, the roots of a Hurwitz polynomial are in the left half of the complex plain, not on the imaginary axis. As for the reason, that is because the polynomial is DEFINED to be one that has that kind of roots.
Wiki User
∙ 13y ago
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What are the values at which the graph of a polynomial crosses the x-axis?
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
Is it true that a polynomial's real roots are the values at which the graph of a polyomial meets the x-axis?
Yes.
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
What is the definition for the zero of a polynomial function?
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
Is the x-intercepts the same thing as zeros?
Yes, the places where the graph of a polynomial intercepts the x-axis are zeros. The value of y at those places must be 0 for the polynomial to intersect the x axis.
What are the values at which the graph of a polynomial crosses the x-axis?
The graph of a polynomial in X crosses the X-axis at x-intercepts known as the roots of the polynomial, the values of x that solve the equation.(polynomial in X) = 0 or otherwise y=0
What is the point at which a graph crosses the x-axis?
For a line, this is the x-intercept. For a polynomial, these points are the roots or solutions of the polynomial at which y=0.
Is it true that a polynomial's real roots are the values at which the graph of a polyomial meets the x-axis?
Yes.
The values at which the graph of a polynomial crosses the x-axis are called roots and are the values for which the y-value is?
zero
How do you find out the number of imaginary zeros in a polynomial?
Descartes' rule of signs (see related link) can help you determine the maximum number of real roots. If the polynomial is odd powered, then there will be at least one real root. Any even powered polynomial can be factored into a bunch of quadratics [though they may not be rational or even pretty], and any odd-powered polynomial can be factored into a bunch of quadratics and one linear (this one would have the real root). So the quadratics may have pairs of real or complex roots (having an imaginary component).To clarify, when I say complex, I'm referring to the fact that there will be an imaginary component to the root, because actually the real numbers is a subset of the set of complex numbers.The order of the polynomial will tell you how many roots it will have. If you can graph the polynomial, then you can see if it crosses the x axis. If it is a 5th order polynomial, and crosses the x axis 3 times, then there are 3 real roots (the other two roots are complex).
What is the greatest number of real roots a polynomial of degree 2 can have?
A real root is when a quadratic equation, or the graph of a polynomial, crosses the x axis, or when the y coordinate is equal to 0. On any polynomial to the degree of two, when graphed the line follows a smooth arc in the shape of a "U" or and upside down "U". Since there are only two prongs to the parabola, or arc, it can only cross the x axis twice, if at all. So there can only be 2 real roots.
How do you find the roots of a polynomial of graphed points?
Join the points using a smooth curve. If you have n points choose a polynomial of degree at most (n-1). You will always be able to find polynomials of degree n or higher that will fit but disregard them. The roots are the points at which the graph intersects the x-axis.
What best describes a root of a polynomial?
A value of the variable when the polynomial has a value of 0. Equivalently, the value of the variable when the graph of the polynomial intersects the variable axis (usually the x-axis).
Are a polynomial's factors the values at which the graph of a polynomial meets the x-axis?
false
How many times does a porabola cross the x-axis when using imaginary numbers?
NONE If both roots are imaginary, the means the parabola does NOT cross the x-axis at all. The place where a function crosses the x- axis has the coordinate (x,0) for some value of x. That means if you plug in x to the function or polynomial, you get 0. This is equivalent to saying that x is a root of the polynomial. But if the only roots are imaginary, there will be no point (x,0) for any real number x.
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.
What is the definition for the zero of a polynomial function?
The zero of a polynomial in the variable x, is a value of x for which the polynomial is zero. It is a value where the graph of the polynomial intersects the x-axis.
