Question

Измени уровненных так чтобы корни остались прежнем

Answer 1

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Answer 2

Changing the Roots of an Equation Without Altering the Values

To change the roots of an equation while keeping the values the same, you can use a transformation method. One common method is to use a linear transformation. This involves multiplying the equation by a non-zero constant, which changes the roots but keeps the values the same.

For example, if the original equation is f(x) = 0, and it has roots x1 and x2, then the transformed equation g(x) = 0 can be obtained by multiplying the original equation by a constant a:

g(x) = a * f(x) = 0

The roots of the transformed equation will be different from the roots of the original equation, but the values of the function at those roots will remain the same.

Example of Linear Transformation

Let's consider an example to illustrate this concept. Suppose the original equation is:

f(x) = (x - 2)(x - 3) = 0

This equation has roots at x = 2 and x = 3. Now, if we want to change the roots while keeping the values the same, we can use a linear transformation. Let's multiply the original equation by a constant a:

g(x) = a * f(x) = a(x - 2)(x - 3) = 0

The roots of the transformed equation g(x) will be different from x = 2 and x = 3, but the values of the function at those roots will remain the same.

Conclusion

In conclusion, to change the roots of an equation while keeping the values the same, you can use a linear transformation by multiplying the original equation by a non-zero constant. This will alter the roots of the equation while preserving the values of the function at those roots.