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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.
Is it true a polynomials real roots are the values at which the graph of a polynomial meets the x axis?
Yes, that is true. The real roots of a polynomial are the values of ( x ) for which the polynomial evaluates to zero, which corresponds to the points where the graph intersects the x-axis. In other words, if ( f(x) = 0 ) for some real number ( x ), then the graph of the polynomial ( f(x) ) will cross the x-axis at that point.
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
Can a fourth degree polynomial touch the x axis three times?
No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.
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 is the maximum number of times that a quadratic function can intersect the x-axis and why?
A quadratic function can intersect the x-axis at most two times. This is because a quadratic function is represented by a polynomial of degree 2, and according to the Fundamental Theorem of Algebra, a polynomial of degree ( n ) can have at most ( n ) real roots. Since the degree is 2 for a quadratic function, it can have either two distinct real roots, one repeated real root, or no real roots at all, leading to a maximum of two x-axis intersections.
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
