Jason solved the quadratic equation x2−4x−12=0

Question

by factoring. His work is shown below.

Step 1: x2−4x−12=0

Step 2: (x-6)(x+2)=0

Step 3: x - 6 = 0, x + 2 = 0

Step 4: x = 6 or x = 2

Step 5: {6,2}

Jason plugged his solutions into the original equation, and found that they did not work. In which step did he first make a mistake?

Answer 1

Let's analyze Jason's work step-by-step:

1. Step 1: The original equation \( x^2 - 4x - 12 = 0 \) is correct.

2. Step 2: He factored the equation as \( (x - 6)(x + 2) = 0 \). To verify this, we can expand \( (x - 6)(x + 2) \):

   \[ (x - 6)(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12 \]

   This step is actually correct.

3. Step 3: From \( (x - 6)(x + 2) = 0 \), he correctly sets each factor to zero:

   • \( x - 6 = 0 \) gives \( x = 6 \)
   • \( x + 2 = 0 \) gives \( x = -2 \)

   Here, he made a mistake in writing down the second solution. It should be \( x = -2 \), not \( x = 2 \).

4. Step 4: He states \( x = 6 \) or \( x = 2 \). This is incorrect because one of the solutions is wrong.

5. Step 5: Jason concludes that the solutions are \( {6, 2} \), which is incorrect.

Therefore, Jason's first mistake occurred in Step 3, where he incorrectly stated the second solution as \( x = 2 \) instead of the correct solution \( x = -2 \).