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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.

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Q: Can Polynomials with the same graph can have different roots?
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Related questions

Polynomials with the same graph can have different roots?

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.


Polynomials with the same roots always have the same graphs?

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You keep them the same if they have different bases


Can Polynomials with the same roots can have different graphs.?

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.


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