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

A x = ±1

B x = ±2

C x = ±1, ±2

D x = 1, 2

✓ Correct Answer: Option C

Let u = x^2. The equation becomes u^2 - 5u + 4 = 0. Factor this quadratic: (u-4)(u-1) = 0. So u=4 or u=1. Since u=x^2, x^2=4 => x=±2, and x^2=1 => x=±1. All are real solutions.

💡 Why is C) the correct answer?

The correct answer to the question "Find all real solutions to the equation x^4 - 5x^2 + 4 = 0." is Option C: x = ±1, ±2.

The other options — A) x = ±1, B) x = ±2, D) x = 1, 2 — are incorrect for this CLEP Exam Prep question. As explained above: Let u = x^2. The equation becomes u^2 - 5u + 4 = 0. Factor this quadratic: (u-4)(u-1) = 0. So u=4 or u=1. Since u=x^2, x^2=4 => x=±2, and x^2=1 => x=±1. All are real solutions.

📚 About This CLEP Exam Prep Practice Question

This 4-level CLEP Exam Prep question from the College Algebra topic is part of BrainForge Quiz's free exam preparation library. Each question includes the correct answer and a detailed explanation to help you understand the underlying concept, not just memorize the answer.

How to use this page: Read the question above, consider all four options (A through D), then check the highlighted correct answer and explanation. For active timed practice, start a free CLEP Exam Prep practice test or use flashcards for spaced repetition review.

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

✓ Correct Answer: Option C

📚 About This CLEP Exam Prep Practice Question

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