Question

.

Answer 1

Find the discriminant first.

Answer 2

And that tells you what?

Does \(\sqrt{37}\) exist in the Real Numbers?

Answer 3

What? Yes it does. \(\sqrt{-37}\) has a little trouble with that. So, it exists. That's a clue.

Answer 4

correct.

Answer 5

What is the discriminant?

Answer 6

In the quadratic formula for finding roots where does the discriminant go?

Answer 7

Please, just write out the Quadratic Formula and look under the Square Root!

Answer 8

\[
D = b^2-4ac\\
\text{ } \\
\frac{ -b \pm \sqrt{b ^{2} - 4ac} }{ 2a } = \frac{ -b \pm \sqrt{D} }{ 2a }
\]

Answer 9

So if you get D = -8 (a negative number) what happens when you plug it into the above formula?

Answer 10

If you take the square root of a negative number you get imaginary or complex numbers.

Answer 11

But how did you come to the conclusion the roots must be real?

Answer 12

The second problem is different from the first problem.