Quadratics with Complex Solutions

Grade 12
Mathematics
N-CN.C.7
Number & Quantity
Free lesson

Aligned to N-CN.C.7 — Common Core State Standards for Mathematics.

What this lesson teaches

When the discriminant b^2 − 4ac is negative, the quadratic formula produces complex solutions containing i. These solutions always come as a conjugate pair.

Worked example

Solve x^2 − 2x + 5 = 0. Here x = (2 ± √(4 − 20))/2 = (2 ± √(−16))/2 = (2 ± 4i)/2 = 1 ± 2i.

Practice questions

Solve x^2 + 9 = 0.
Solve x^2 + 1 = 0.
Solve x^2 − 4x + 13 = 0 using the quadratic formula.

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Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.

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En español

Cuadráticas con soluciones complejas

Cuando el discriminante b^2 − 4ac es negativo, la fórmula cuadrática produce soluciones complejas que contienen i. Estas soluciones siempre aparecen como un par conjugado.

Ejemplo: Resuelve x^2 − 2x + 5 = 0. Aquí x = (2 ± √(4 − 20))/2 = (2 ± √(−16))/2 = (2 ± 4i)/2 = 1 ± 2i.

More Number & Quantity lessons

Adding and Multiplying Complex NumbersN-CN.A.2 The Fundamental Theorem of AlgebraN-CN.C.9 Finding Vector ComponentsN-VM.A.2 Adding and Subtracting VectorsN-VM.B.4 Representing Data with MatricesN-VM.C.6 Matrix Addition and MultiplicationN-VM.C.8

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