Quadratic Equation/Examples/x^2 + 4 = 0

Example of Quadratic Equation

The quadratic equation:

$x^2 + 4 = 0$

has the wholly imaginary roots:

$x = \pm 2 i$

where $i = \sqrt {-1}$ is the imaginary unit.

Proof

From the Quadratic Formula:

\(\ds x^2 + 4\)

\(=\)

\(\ds 0\)

\(\ds \leadsto \ \ \)

\(\ds x\)

\(=\)

\(\ds \dfrac {-0 \pm \sqrt {0^2 - 4 \times 1 \times 4} } {2 \times 1}\)

Quadratic Formula

\(\ds \)

\(=\)

\(\ds \dfrac {\pm \sqrt {-4} } 2\)

\(\ds \)

\(=\)

\(\ds \pm 2 i\)

Definition of Imaginary Unit

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): complex number
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): complex number