Quadratics with Complex Solutions
Aligned to N-CN.C.7 — Common Core State Standards for Mathematics.
What this lesson teaches
When a quadratic with real coefficients has a negative discriminant, its solutions are complex. The quadratic formula still works — the square root of the negative number produces the imaginary part.
Worked example
Solve x^2 − 4x + 13 = 0. Using x = (−b ± √(b^2 − 4ac))/(2a): x = (4 ± √(16 − 52))/2 = (4 ± √(−36))/2. Since √(−36) = 6i, x = (4 ± 6i)/2 = 2 ± 3i.
Practice questions
- Solve x^2 + 9 = 0.
- Solve x^2 − 2x + 5 = 0.
- Solve x^2 + 6x + 10 = 0.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Cuadráticas con Soluciones Complejas
Cuando una ecuación cuadrática con coeficientes reales tiene discriminante negativo, sus soluciones son complejas. La fórmula cuadrática sigue funcionando — la raíz cuadrada del número negativo produce la parte imaginaria.
Ejemplo: Resuelve x^2 − 4x + 13 = 0. Usando x = (−b ± √(b^2 − 4ac))/(2a): x = (4 ± √(16 − 52))/2 = (4 ± √(−36))/2. Como √(−36) = 6i, x = (4 ± 6i)/2 = 2 ± 3i.
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