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Doctor Mode Analysis

Clinical feedback on your problem-solving approach

What Appu Noticed

Based on your recent practice session

During your last practice session, you attempted to solve x² + 5x + 6 = 0 using the quadratic formula but arrived at an incorrect answer. The error occurred in the substitution step when identifying the coefficient values.

Your Attempt

Given equation: x² + 5x + 6 = 0

You identified:

  • a = 1 ✓
  • b = 5 ✓
  • c = -6 ✗ (Should be +6)

This led to calculating: x = (-5 ± √49) / 2

Breakdown: What Went Wrong

1

Misidentified the constant term

You wrote c = -6, but in the equation x² + 5x + 6 = 0, the constant term is +6 (not -6). The sign must match exactly as it appears in standard form.

2

Incorrect discriminant calculation

Because c was wrong, the discriminant b² - 4ac became 25 - 4(1)(-6) = 49 instead of the correct value: 25 - 4(1)(6) = 1.

The Correct Way to Think

Systematic Approach:

  1. Step 1:Write the equation in standard form: ax² + bx + c = 0
  2. Step 2:Identify coefficients by matching positions (not by guessing signs)
  3. Step 3:a = 1 (coefficient of x²), b = 5 (coefficient of x), c = 6 (constant)
  4. Step 4:Calculate discriminant: 5² - 4(1)(6) = 25 - 24 = 1
  5. Step 5:Apply formula: x = (-5 ± 1) / 2 → x = -2 or x = -3

Side-by-Side Comparison

❌ Your Approach

  • • Misread constant sign
  • • c = -6 (incorrect)
  • • Discriminant = 49
  • • Final answer: x = 1 or x = 6

✓ Correct Approach

  • • Matched equation to standard form
  • • c = +6 (correct)
  • • Discriminant = 1
  • • Final answer: x = -2 or x = -3

Fix-It Practice

Answer these quick questions to confirm your understanding:

1. In the equation 3x² - 7x + 2 = 0, what is the value of c?

2. What is the discriminant of x² + 4x + 4 = 0?

3. If the discriminant is negative, how many real solutions exist?