Question

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

Answer 1

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

Answer 2

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`