The zeros of the equation 3x² - 4 = -x⁴ are 1, -1, 2i, -2i.
Hence option D is the right choice.
What is an equation?
An assertion of equivalence between two expressions containing variables and/or numbers is known as an equation.
What are zeros of a function?
The zeros of an equation are the set of values, for which the equation attains a value = 0.
How do we solve the given question?
We are asked to find the zeros of the equation 3x² - 4 = -x⁴.
We first simplify the equation by adding x⁴ on both sides of the equation.
∴ 3x² - 4 + x⁴ = -x⁴ + x⁴
or, x⁴ + 3x² - 4 = 0.
Now, we factorize the above equation.
x⁴ + 4x² - x² - 4 = 0
or, x²(x² + 4) -1(x² + 4) = 0
or, (x² - 1)(x² + 4) = 0.
By the zero-product rule,
Either,
Or,
- x² + 4 = 0
- x² = -4
- x² = ±√-4 = ±2√-1 = ±2i (∵ √-1 = i, complex number)
- Either x = 2i, Or x = -2i.
∴ The zeros of the equation 3x² - 4 = -x⁴ are 1, -1, 2i, -2i.
Hence option D is the right choice.
Learn more about the zeros of an equation at
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