What are the solutions to the equation 0x² + 6? Check all that apply.

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Understanding the Equation

The equation given is 0x² + 6 = 0. Let’s break it down:

  • In this equation, 0x² signifies that the coefficient of x² is zero. This means that the term involving x does not contribute to the equation.
  • Thus, the equation simplifies to 6 = 0, which is clearly incorrect.

Analyzing the Solutions

Since the equation simplifies to a false statement (6 cannot equal 0), it follows that there are no possible values of x that can satisfy this equation.

In mathematical terms, such equations are often referred to as inconsistent and do not have any real solutions.

Conclusion

In conclusion, the solutions to the equation 0x² + 6 = 0 are:

  • No solutions (or the empty set, ∅).

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