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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.
How are adding and multiplying polynomials different from each other?
Adding polynomials involves combining like terms by summing their coefficients, resulting in a polynomial of the same degree. In contrast, multiplying polynomials requires applying the distributive property (or FOIL for binomials), which results in a polynomial whose degree is the sum of the degrees of the multiplied polynomials. Essentially, addition preserves the degree of the polynomials, while multiplication can increase it.
What is the homonym of routes?
The homonym of "routes" is "roots." They sound the same but have different meanings.
Can The graphs of two different direct variations can be parallel?
No, the graphs of two different direct variations cannot be parallel. Direct variation is represented by the equation ( y = kx ), where ( k ) is the constant of variation. For two direct variations to be parallel, they would need to have the same slope, which means they would have the same value of ( k ). However, since the variations are different, they must have different values of ( k ), resulting in non-parallel graphs.
What is it called when A set of equations that have the same variable?
Polynomials
