What value of x satisfies the equation 3x^4 + 5x^2 = 0?

To solve the equation 3x⁴ + 5x² = 0, we can start by factoring out the common term.

First, notice that both terms on the left side contain a factor of x². We can factor this out:

3x4 + 5x2 = x2(3x2 + 5) = 0

Next, we set each factor equal to zero:

• x² = 0
• 3x² + 5 = 0

For the first equation x² = 0, we take the square root of both sides:

x = 0

For the second equation 3x² + 5 = 0, we can solve for x²:

3x2 = -5

Since 3x² cannot be negative (because x² is always non-negative), there’s no real solution from this part.

Thus, the only solution to the original equation is:

x = 0

In conclusion, the value of x in the solution set of the equation 3x⁴ + 5x² = 0 is:

x = 0