Question

Identify the solutions of 3+4x2−13−−−−−−√3=−5
3
+
4
𝑥
2
−
13
3
=
−
5
.(1 point)
Responses

13−−√
13
, −13−−√
−
13
Start Root 13 End Root , negative Start Root 13 End Root

21−−√
21
, −21−−√
−
21
Start Root 21 End Root , negative Start Root 21 End Root

5–√
5
, −5–√
−
5
Start Root 5 End Root , negative Start Root 5 End Root

23–√
2
3
, −23–√

Answer 1

To find the solutions of the equation

\[
\sqrt{3 + 4x^2 - 13} = -5,
\]

let's start by simplifying the left side:

\[
\sqrt{4x^2 - 10} = -5.
\]

Since the square root function cannot output a negative number, there are no real solutions to this equation.

Thus, the options given, such as \(\sqrt{13}\), \(-\sqrt{13}\), \(\sqrt{21}\), \(-\sqrt{21}\), \(\sqrt{5}\), \(-\sqrt{5}\), or \(\sqrt{23}\), do not apply because the equation cannot be satisfied.

The proper conclusion is that there are no solutions.