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kondaur [170]
2 years ago
8

Find an equation with a solution of x = 2 of multiplicity 1 , and a solution of x = − 1 of multiplicity 2 .

Mathematics
1 answer:
luda_lava [24]2 years ago
7 0

We want to find an equation for the given solutions and the multiplicity of each solution.

The equation is:

0 = (x - 2)*(x + 1)^2

First, assume that we have a given equation and we know that we have solutions {x₁, x₂, ..., xₙ}, each one with multiplicity {m₁, ..., mₙ}.

The equation, of a polynomial that meets these requirements, is given by:

0 = A*(x - x_1)^{m_1}*...*(x - x_n)^{m_n}

Where A is the leading coefficient and can be any real number.

Now that we know that, here we have the solutions:

  • x = 2 with multiplicity 2
  • x = -1 with multiplicity 2

We don't have information about the leading coefficient, so we assume it is equal to 1.

Then the equation is:

0 = (x - 2)*(x + 1)^2

If you want to learn more, you can read:

brainly.com/question/11536910

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