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

2 Answers
Mar 22, 2018

Answer:

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

Explanation:

The discriminant is #b^2 - 4xxaxxc" "#, and the form of that equation is #ax^2 + bx + c#. Therefore the discriminant is

#0^2 - 4xx1xx25 = -100#
.
Therefore the discriminant is -100. This means that the equation has 0 solutions.

Discriminant #> 0 -> 2# Solutions
Discriminant# = 0color(white)(.)-> 1# Soltion
Discriminant #< 0 -> 0# Solutions

Mar 22, 2018

Answer:

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=ax^2+bx+c=0#

The formula is #x=(-b+-sqrt(b^2-4ac))/(2a)#

The determinate is the part #b^2-4ac#

Write the given equation as: #y=x^2+0x+25=0#

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

So the determinate #->0^2-4(1)(25)=-100#

so we end up with #sqrt(-100)#

As this is negative we have a complex number solution.

That is #x inCC#