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(x+2)^2*(x-7)*(x+5) 0

2 min read Jun 16, 2024
(x+2)^2*(x-7)*(x+5) 0

Solving the Equation (x+2)^2*(x-7)*(x+5) = 0

This equation is a polynomial equation and we can solve it by finding the values of x that make the equation true.

Understanding the Equation

  • The equation is set to zero. This means we are looking for the points where the expression on the left-hand side equals zero.
  • The expression is a product of four factors: (x+2)^2, (x-7), and (x+5).

The Zero Product Property

The key to solving this equation is the Zero Product Property: If the product of two or more factors is zero, then at least one of the factors must be zero.

Solving for x

To find the solutions, we set each factor equal to zero and solve for x:

  1. (x+2)^2 = 0

    • Take the square root of both sides: x + 2 = 0
    • Solve for x: x = -2

  2. (x-7) = 0

    • Solve for x: x = 7

  3. (x+5) = 0

    • Solve for x: x = -5

The Solutions

Therefore, the solutions to the equation (x+2)^2*(x-7)*(x+5) = 0 are:

  • x = -2 (This solution has a multiplicity of 2 because the factor (x+2) appears squared.)
  • x = 7
  • x = -5

Conclusion

The equation (x+2)^2*(x-7)*(x+5) = 0 has three solutions: x = -2, x = 7, and x = -5. These are the values of x that make the expression on the left-hand side equal to zero.

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