Question

The roots of the equation \( x^4 - 5x^2 + 4 = 0 \) are

• A. -2, 1, -2, -1
• B. 2, -1, -2, 1
• C. -2, -1, -1, -2
• D. 2, 1, 1, 2

Hint:

When solving quadratic equations in terms of \( x^2 \), make sure to consider both positive and negative square roots.

Answer 1

The Correct Option is B

Step 1: Rewriting the equation.
The given equation is \( x^4 - 5x^2 + 4 = 0 \). Let \( y = x^2 \), so the equation becomes: \[ y^2 - 5y + 4 = 0 \]

Step 2: Solving the quadratic equation.
Now, solve the quadratic equation \( y^2 - 5y + 4 = 0 \) by factoring: \[ (y - 1)(y - 4) = 0 \] So, \( y = 1 \) or \( y = 4 \).

Step 3: Substituting \( y = x^2 \).
Since \( y = x^2 \), we substitute back to find the roots of \( x \):
- For \( y = 1 \), \( x^2 = 1 \), so \( x = 1 \) or \( x = -1 \).
- For \( y = 4 \), \( x^2 = 4 \), so \( x = 2 \) or \( x = -2 \).

Step 4: Conclusion.
Therefore, the roots of the equation are \( 2, -1, -2, 1 \).

Final Answer: 2, -1, -2, 1.