#46
Top 50 Mistake
Sign errors in the quadratic formula H
"The Formula Fumble"
The Mistake in Action
Solve $x^2 - 4x - 5 = 0$ using the quadratic formula.
Wrong: $a = 1, b = 4, c = -5$ $x = \frac{-4 \pm \sqrt{16 + 20}}{2}$
Why It Happens
Students misread the coefficient $b$ when the term is negative. In $x^2 - 4x - 5$, we have $b = -4$, not $b = 4$.
The Fix
Write out $a$, $b$, $c$ carefully, including signs.
For $x^2 - 4x - 5 = 0$:
- $a = 1$
- $b = -4$ (the coefficient of $x$, including the negative)
- $c = -5$
$$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-5)}}{2(1)}$$ $$x = \frac{4 \pm \sqrt{16 + 20}}{2} = \frac{4 \pm 6}{2}$$ $$x = 5 \text{ or } x = -1$$
Spot the Mistake
Can you identify where this student went wrong?
For $x^2 - 4x - 5 = 0$:
$a = 1, b = 4, c = -5$
$x = \frac{-4 \pm \sqrt{16+20}}{2}$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: