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

May 21, 2015

Your equation is in the form $a {x}^{2} + b x + c = 0$ where:
$a = 2$
$b = 0$
$c = 0$
The discriminant is:
$\Delta = {b}^{2} - 4 a c = 0 - 0 = 0$
When $\Delta = 0$ you will have two real coincident solutions.
In this case ${x}_{1} = {x}_{2} = 0$

May 21, 2015

The discriminant for a parabolic equation of the form
$a {x}^{2} + b x + c = 0$
is
$\Delta = {b}^{2} - 4 a c$

$\Delta \left\{\begin{matrix}< 0 \rightarrow \text{no Real solutions" \\ =0 rarr "1 Real solution" \\ >0 rarr "2 Real solutions}\end{matrix}\right.$

$y = 2 {x}^{2}$
can be re-written in the form $y = a {x}^{2} + b x + c$ as

$y = 2 {x}^{2} + \left(0\right) x + \left(0\right)$

and the discriminant becomes
$\Delta = {0}^{2} - 4 \left(2\right) \left(0\right) = 0$
which implies
there is 1 Real solution.