#44
Top 50 Mistake
Only giving one solution to a quadratic
"The Missing Root"
The Mistake in Action
Solve $x^2 - 9 = 0$
Wrong: $x^2 = 9$ $x = 3$
Why It Happens
Students find one square root and stop. They forget that both positive and negative values square to give a positive result.
The Fix
When you take a square root, always consider both the positive and negative roots.
$x^2 = 9$ $x = \pm\sqrt{9}$ $x = 3$ or $x = -3$
Check: $3^2 = 9$ ✓ and $(-3)^2 = 9$ ✓
Memory aid: "Square roots come in pairs — positive and negative!"
Spot the Mistake
Can you identify where this student went wrong?
$x^2 - 9 = 0$
$x^2 = 9$
$x = 3$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: