# How to use the discriminant to find out what type of solutions the equation has for x^2 + 25 = 0?

Mar 22, 2018

The discriminant equals -100. Therefore the equation has 0 solutions.

#### Explanation:

The discriminant is ${b}^{2} - 4 \times a \times c \text{ }$, and the form of that equation is $a {x}^{2} + b x + c$. Therefore the discriminant is

${0}^{2} - 4 \times 1 \times 25 = - 100$
.
Therefore the discriminant is -100. This means that the equation has 0 solutions.

Discriminant $> 0 \to 2$ Solutions
Discriminant$= 0 \textcolor{w h i t e}{.} \to 1$ Soltion
Discriminant $< 0 \to 0$ Solutions

Mar 22, 2018

The solution type for this question is such that it belongs to the 'Complex' number set of values.

The graph does NOT cross the x-axis

#### Explanation:

Consider the standardised form of $y = a {x}^{2} + b x + c = 0$

The formula is $x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$

The determinate is the part ${b}^{2} - 4 a c$

Write the given equation as: $y = {x}^{2} + 0 x + 25 = 0$

In this case: a=1; b=0 and c=25

So the determinate $\to {0}^{2} - 4 \left(1\right) \left(25\right) = - 100$

so we end up with $\sqrt{- 100}$

As this is negative we have a complex number solution.

That is $x \in \mathbb{C}$