# How do you find the discriminant and how many solutions does x^2+2x+7=0 have?

Apr 30, 2015

The equation is of the form color(blue)(ax^2+bx+c=0 where:

$a = 1 , b = 2 , c = 7$

The Disciminant is given by :
$\Delta = {b}^{2} - 4 \cdot a \cdot c$
$= {\left(2\right)}^{2} - 4 \cdot 1 \cdot 7$
$= 4 - 28 = - 24$

If $\Delta = 0$ then there is only one solution.
(for $\Delta > 0$ there are two solutions,
for $\Delta < 0$ there are no real solutions)

As $\Delta < 0$, this equation has NO REAL SOLUTIONS

• Note:
The solutions are normally found using the formula
$x = \frac{- b \pm \sqrt{\Delta}}{2 \cdot a}$