# Write a quadratic equation with one solution

The square root of b squared is b, and the square root of is So this right here is There's not going to be this plus or minus, it's not going to be relevant. We can find b though, because they gave us a clue. This is just the square root of 0, and the square root of 0 is just 0. They told us that this quadratic equation only has one solution. It's going to have a square root.

## Determine the nature of the solutions to the equation: x2 + 2x - 4 = 0

We just have to evaluate b squared minus 4ac. So let's think about it in the context of this equation right here. Now what happens if b squared minus 4ac is equal to 0? That's that part of the quadratic equation. Well if b squared minus 4ac is less than 0, this is going to be a negative number right here and you're going to have to take the square root of a negative number. Now that we know b is, we can use the quadratic formula to find our solution. But what I want to do here is actually explore the quadratic formula, and think about how we can determine the number of solutions without even maybe necessarily finding them explicitly. If this expression under the radical is equal to 0, you're just going to have the square root of 0. You're only going to have one solution. So it's only going to have one solution. That will be the number of solutions. If b squared minus 4ac is greater than 0, what's going to happen? So it's going to be negative b plus or minus 0. And negative b is-- we could just solve it. So this right here is

Now what happens if b squared minus 4ac is equal to 0? We could just apply the quadratic formula. We could factor it and just figure out the values of x that satisfy it and just count them.

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