Question

The sum of the squares of all the roots of the equation \( x^2 + [2x - 3] - 4 = 0 \) is:

• A. \(3(2 - \sqrt{2})\)
• B. \(6(2 - \sqrt{2})\)
• C. \(3(3 - \sqrt{2})\)
• D. \(6(3 - \sqrt{2})\)

Hint:

Always remember to check both roots in quadratic equations for full solutions.

Answer 1

The Correct Option is D

Step 1: Find the roots.
The roots are \( \sqrt{2} \) and \( 3 - \sqrt{2} \).
Step 2: Compute the sum of squares.
The sum of squares is calculated as \( (\sqrt{2})^2 + (3 - \sqrt{2})^2 = 2 + (9 + 2 - 6\sqrt{2}) = 13 - 6\sqrt{2} \).
Conclusion: Therefore, the sum of the squares of the roots is \( 6(3 - \sqrt{2}) \).