How many zeros does a polynomial have if it cuts the x-axis at 3 points?

Since the given polynomial cuts the x-axis at 3 points, the number of zeroes is 3.

Can a polynomial not cross the x-axis?

The multiplicity of a root affects the shape of the graph of a polynomial. Specifically, If a root of a polynomial has odd multiplicity, the graph will cross the x-axis at the the root. If a root of a polynomial has even multiplicity, the graph will touch the x-axis at the root but will not cross the x-axis.

How many times the graph of a cubic polynomial will cut the horizontal x-axis?

A graph of cubic polynomial can cut the x-axis at 3 points because cubic polynomial has maximum 3 zeroes.

How many zeroes does a polynomial have if it cuts the Y axis at 2 points?

no. of zeros of polynomial will be 1. Step-by-step explanation: number of zeros will be 1 as it cut X-axis or Y-axis only one time….

What is the quadratic polynomial whose sum and the product of zeroes is √ 2 ⅓ respectively?

Sum and product of whose zeros are √2 and 1/3 respectively. where k/3 is a constant term, real number. respectively. Hence, required polynomial is 4×2 + x + 1.

What does it mean if a graph does not touch the X axis?

Touching the x axis at x=a means the function has a root at x=a and not touching means it doesn’t. If we restrict ourselves only to polynomials (a very small class of functions) then having a root/touching the axis at x=a means x−a is a factor of the polynomial p(x).

How do you determine if a graph crosses or touches the X axis?

If the graph crosses the x-axis and appears almost linear at the intercept, it is a single zero. If the graph touches the x-axis and bounces off of the axis, it is a zero with even multiplicity. If the graph crosses the x-axis at a zero, it is a zero with odd multiplicity.

How many times does a cubic function cross the x-axis?

The graph of a cubic must cross the x-axis at least once giving you at least one real root. So, any problem you get that involves solving a cubic equation will have a real solution. given that x = −2 is a solution.

How many zeros does the graph of the polynomial function have?

A polynomial function may have zero, one, or many zeros. All polynomial functions of positive, odd order have at least one zero, while polynomial functions of positive, even order may not have a zero.

Which of the following is not a graph of quadratic polynomial?

Summary: Option D is not the graph of a quadratic polynomial.

How many zeros does a polynomial p(x) have?

In general, Given a polynomial p (x) of degree n, the graph of y = p (x) intersects the x-axis at a maximum of n points. Therefore, a polynomial p (x) of degree n has a maximum of n zeroes. Question 1: The graphs of y = p (x) are given in the figure below, for some polynomials p (x).

Does the graph of a polynomial of even degree intersect the x-axis?

It may easily happen that the graph of a polynomial of even degree does not intersect the x-axis. In any case, for any function p, and a given value a, if p (a)=0, then by definition a is a zero of p and (a,0) is a point on the graph of p, and therefore p intersects the x-axis at a.

How do you graph two cubic polynomials with two zeroes?

Let’s plot the graph of the following two cubic polynomials: The graphs of y = x 3 and y = x 3 – x 2 look as follows: From the first graph, you can observe that 0 is the only zero of the polynomial x 3, since the graph of y = x 3 intersects the x-axis only at 0. Similarly, the polynomial x 3 – x 2 = x 2 (x – 1) has two zeroes, 0 and 1.

Where does the graph cut the x-axis?

The graph cuts x-axis at two distinct points A and A′, where the x-coordinates of A and A′ are the two zeroes of the quadratic polynomial ax 2 + bx + c, as shown below: The graph intersects the x-axis at only one point, or at two coincident points.