# How do you use the discriminant to determine the numbers of solutions of the quadratic equation x^2 + 6x - 7 = 0 and whether the solutions are real or complex?

Feb 5, 2016

see explanantion

#### Explanation:

Consider the following value for the discriminant: (d)

$d > 0 \to$The plot crosses the x-axis so has 2 solutions

$d = 0 \to$The plot is such that it does not cross the x-axis but the$\text{ }$ axis forms a tangent to the max/min

$d < 0 \to$The plot does not cross nor come into contact with the $\text{ }$x-axis. Thus any solution to the expression being $\text{ }$equated to zero will result in a complex number solution.

For your equation of: ${x}^{2} + 6 x - 7 = 0$

The discriminant is:

$\sqrt{{b}^{2} - 4 a c} \to \sqrt{{6}^{2} - 4 \left(1\right) \left(- 7\right)}$

$\sqrt{{6}^{2} + 28} \text{ ">" "0" " =>" " 2" solutions}$

As these are not complex they are real solutions