How to use the discriminant to find out what type of solutions the equation has for x^2 + 25 = 0x2+25=0?

2 Answers
Petersmitty · Tony B
Mar 22, 2018

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

Explanation:

The discriminant is b^2 - 4xxaxxc" "b2−4×a×c , and the form of that equation is ax^2 + bx + cax2+bx+c. Therefore the discriminant is

0^2 - 4xx1xx25 = -10002−4×1×25=−100
.
Therefore the discriminant is -100. This means that the equation has 0 solutions.

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

Tony B
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=ax^2+bx+c=0y=ax2+bx+c=0

The formula is x=(-b+-sqrt(b^2-4ac))/(2a)x=−b±√b2−4ac2a

The determinate is the part b^2-4acb2−4ac

Write the given equation as: y=x^2+0x+25=0y=x2+0x+25=0

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

So the determinate ->0^2-4(1)(25)=-100→02−4(1)(25)=−100

so we end up with sqrt(-100)√−100

As this is negative we have a complex number solution.

That is x inCC

Related questions
See all questions in Solutions Using the Discriminant
Impact of this question
2419 views around the world
You can reuse this answer
Creative Commons License