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If you only look at the value of the roots and not their multiplicity then the answer is yes.
The straight line y = x - 1 and the parabola y = (x - 1)^2 have the same root: x = 1. But the graphs are obviously different. All polynomials of the form y = (x - 1)^n will have x = 1 as the only root but they will have different shapes. The reason to this is that in the case of the straight line it is a root of multiplicity 1, in the case of a parabola it is a root of multiplicity 2 and in the case of y = (x - 1)^n it is a root of multiplicity n.
What else can I help you with?
Polynomials with the same roots always have the same graphs?
false
Can polynomials with the same graph have different roots?
False! If the graph is exactly the same, then the x-intercepts will be the same which implies the roots are them same. However, you can have the same roots and different graphs. So while the first statement is true, the converse if not.
Is it true or false that Polynomials with the same graph can have different roots.?
True. Polynomials can have the same graph if they differ only by a constant factor. For example, the polynomials ( f(x) = x^2 - 1 ) and ( g(x) = 2(x^2 - 1) ) have the same graph, but their roots are the same. However, different polynomials can share the same graph at certain intervals or under specific transformations, leading to the possibility of having different roots.
When adding polynomials what do you do to the exponents?
You keep them the same if they have different bases
Polynomials have factors that are?
Other polynomials of the same, or lower, order.
How are line plots and line graphs the same?
They are different names for the same thing!
Homo graphs are words that are?
spelled the same but have different meanings
Is binomial and polynomials the same?
No.
What is the homonym of routes?
The homonym of "routes" is "roots." They sound the same but have different meanings.
What is it called when A set of equations that have the same variable?
Polynomials
Imagine you shot a cannonball and threw a baseball into the air at the same speed and to the same height Would the graphs of their paths be the same or different?
they would be in a vacuum
What are the rules in addition of polynomials?
Add together the coefficients of "like" terms. Like terms are those that have the same powers of the variables in the polynomials.
