Find all real solutions to the equation x^4 - 5*x^2 + 4 = 0.

Answer and explanation

Correct answer: B. x = 1, -1, 2, and -2

  1. Step 1: Let u = x^2. The equation becomes u^2 - 5*u + 4 = 0.
  2. Step 2: Factor: (u - 1)(u - 4) = 0, so u = 1 or u = 4.
  3. Step 3: From u = x^2 = 1: x = 1 or x = -1.
  4. Step 4: From u = x^2 = 4: x = 2 or x = -2.
  5. Step 5: The four real solutions are x = 1, -1, 2, and -2.
Answer
x = 1, -1, 2, and -2.
Why not the others: x = 1 and 2 only neglects the negative square roots; x = 4 and 1 are the values of u, not x; x = +-2, +-4 confuses roots of u with x.

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