Solution Set Math Example 4

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Example 4

medium
What is the solution set of x2+1=0x^2 + 1 = 0 over the real numbers?

Solution

  1. 1
    x2=−1x^2 = -1 has no real solution since x2≥0x^2 \geq 0 for all real xx.
  2. 2
    Solution set: ∅\emptyset (the empty set).

Answer

∅\emptyset
When no real number satisfies the equation, the solution set is empty. The square of any real number is non-negative, so x2=−1x^2 = -1 has no real solutions.

About Solution Set

The complete set of all values that satisfy a given equation or inequality — it may be empty, finite, or infinite.

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Example 1 easy

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Example 2 medium

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Example 3 easy

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