How to use the discriminant to find out what type of solutions the equation has for x^2 + 2x + 5 = 0?

1 Answer
Jun 7, 2015

${x}^{2} + 2 x + 5 = 0$

The Discriminant is given by:
$\Delta = {b}^{2} - 4 \cdot a \cdot c$

$= {\left(2\right)}^{2} - \left(4 \cdot 1 \cdot 5\right)$

$= 4 - 20 = - 16$

• For $\Delta = 0$ then there is only one solution.
• For $\Delta > 0$ there are two solutions,
• For $\Delta < 0$ there are no real solutions

As $\Delta = - 16$, this equation has NO REAL SOLUTIONS
- Note :
The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$

As $\Delta = - 16$, $x = \frac{\left(- 2\right) \pm \sqrt{- 16}}{2 \cdot 1} = \frac{- 2 \pm \sqrt{- 16}}{2}$