Question

Solve each question with the quadratic formula
6a² + 10 = 0


I know the answer but I'm not to sure how imaginary roots work. I would really appreciate if someone could explain how imaginary roots work! :)

Answer 1

Hello!

Do you have the simplified square root before where you got stuck? / after you plug into the quadratic formula?

Answer 2

\[\frac{ \sqrt{-240} }{ 12 }\]

Answer 3

wonderful

are you aware of how to simplify square roots without worrying about the negative?

Answer 4

for example:
\(\sqrt{12}=\sqrt{4*3}=2\sqrt{3}\)

but you do it with
\(\sqrt{240}\)

Answer 5

\[\sqrt{240}=\sqrt{4*4*15}=4\sqrt{15}\]

Answer 6

perfect!
this means that
\(\sqrt{-240}=4\sqrt{-15}\)

Answer 7

now, the only thing different with the imaginary stuff is... \(\sqrt{-1}=i\)
so \(\sqrt{-15}=\sqrt{-1*15}=i~\sqrt{15}\)

Answer 8

would it be written as \[4i \sqrt{15}\]or\[4\sqrt{15}i\]

Answer 9

for handwriting purposes, everything not under the squareroot should go in front of the squareroot, just in case you draw it too long on the paper by accident

Answer 10

so you would then have \[\frac{-0± 4i \sqrt{15} }{ 12 }\] which can be simplified to \[\frac{ 0±i \sqrt{15} }{ 3 }\] which is the final answer?

Answer 11

you might not need the 0 in your final answer, but that is correct :)

Answer 12

thanks