Numerical answer
The roots of the quadratic equation x² − 11x + k = 0 differ by 3. What is the value of k?
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Answer: 28
Let the roots be α and β. Then α + β = 11 and α − β = 3.
Solving: α = 7, β = 4. Product of roots = k = 7 × 4 = 28.
Alternative: (α − β)² = (α + β)² − 4αβ → 9 = 121 − 4k → k = 28.
Solving: α = 7, β = 4. Product of roots = k = 7 × 4 = 28.
Alternative: (α − β)² = (α + β)² − 4αβ → 9 = 121 − 4k → k = 28.
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