Question

-4 +_ square root 2^2-4(1)(3) divided by 2(1)

Answer 1

What is one solution of the above quadratic equation?(1 point)
Responses

(-3,0)
(-3,0)

(-4,0)
(-4,0)

(0,3)
(0,3)

(-2,-1)

Answer 2

To solve the expression you've provided, we can break it down step by step. It appears to resemble the quadratic formula. The expression looks like this:

\[
-4 \pm \sqrt{2^2 - 4(1)(3)} \div 2(1)
\]

Let's simplify it:

1. Calculate \(2^2\):
\[
2^2 = 4
\]

2. Calculate \(4(1)(3)\):
\[
4 \cdot 1 \cdot 3 = 12
\]

3. Now, substitute these values back into the expression beneath the square root:
\[
4 - 12 = -8
\]

Now the expression becomes:

\[
-4 \pm \sqrt{-8} \div 2(1)
\]

4. Simplifying \(\sqrt{-8}\):
\[
\sqrt{-8} = \sqrt{8}i = \sqrt{4 \cdot 2}i = 2\sqrt{2}i
\]

So now substituting this back into the expression gives:

\[
-4 \pm 2\sqrt{2}i \div 2
\]

5. Now, simplify the division by 2:
\[
(-4 \pm 2\sqrt{2}i) \div 2 = -2 \pm \sqrt{2}i
\]

Therefore, the final result is:

\[
-2 \pm \sqrt{2}i
\]

Answer 3

To find one solution of the quadratic equation you were referring to, which is likely related to the expression we discussed earlier, we need to clarify a bit more about the quadratic itself.

The quadratic formula derived from the expression you indicated is:

\[
x = -2 \pm \sqrt{2}i
\]

This means that the two solutions of the quadratic equation are complex:

1. \(x = -2 + \sqrt{2}i\)
2. \(x = -2 - \sqrt{2}i\)

However, the options you provided:

- (-3,0)
- (-4,0)
- (0,3)
- (-2,-1)

are all points likely in the Cartesian plane. None of the complex solutions match any of the given points, as all those points imply real solutions.

If you were looking for real number solutions, then none of the provided options match. However, the point that seems closest in terms of \(x\)-coordinate (though not a solution) is:

- **(-2,-1)**

If the context is strictly about finding points from your options, then **(-2,-1)** could work if you're merely asking which point relates most closely (as it shares the \(x\)-value of -2). Please clarify if you're searching for complex roots specifically or real solutions in another context!