Question

How many and of what type are the solutions to x2 + 10x + 25 = 0?

No real solutions

Two identical rational solutions

Two different rational solutions

Two irrational solutions

Answer 1

Please… factor this.

Answer 2

Well, you could factor, OR you could use the discriminant, which is simpler.

Answer 3

The discriminant is just the thing inside the square root in the quadratic formula, or b^2-4ac.

Answer 4

how do i use the discriminant?

Answer 5

If your discriminant (D) is 0, then you have 2 identical solutions.

Answer 6

If it's negative, you have two different solutions that are IMAGINARY.

Answer 7

If it's positive but a square number, then it's two different rational solutions.

Answer 8

And lastly, if it's positive but not square-rootable, then it's two different irrational solutions.

Answer 9

Really, it makes sense. If you think about it.

Answer 10

Anyway, b^2-4ac = 10^2 - 4(1)(25) = 100-100=0.

Answer 11

OOH! The Discriminant is 0! That means that you have...?

Answer 12

2 identical solutions

Answer 13

@OakTree is correct. The discriminant is faster. But you need to learn to factor, and that is an art (also a lot more fun).

Answer 14

Good.

Answer 15

The discriminant is a very useful tool, but remember that it won't tell you what the actual roots are. For that, you need the actual quadratic formula.

Answer 16

Or factoring. :)

Answer 17

okay thank you!