Write the equation that has the given roots.
Roots: 1 with multiplicity of 2 and -1
How do you figure it out?
If I understand you, the root of 1 appears twice,
equation : (x-1)(x-1)(x+1) = 0
To find the equation with the given roots, you can start by using the fact that the roots of a polynomial equation are the values of x that make the equation equal to zero.
Given that the roots are 1 with a multiplicity of 2 and -1, we can say that the factors of the equation will be (x-1)(x-1)(x+1).
To obtain the equation, we multiply these factors together:
(x-1)(x-1)(x+1) = (x-1)^2(x+1)
Expanding this expression further, we have:
(x-1)^2(x+1) = (x-1)(x-1)(x+1) = (x^2 - 2x + 1)(x+1)
So, the equation with roots 1 with a multiplicity of 2 and -1 is (x^2 - 2x + 1)(x+1).