Question

(3x⁴ + 2x² - 6) - (4x⁴ - 2x² - 6)​

Answer 1

Step-by-step explanation:

3 * (x^4) - 2 * (x^2) - 1 = 0

3 * (x^4) - 3 * (x^2) + (x^2) - 1 = 0

{3 * (x^2) + 1} * {(x^2) - 1} = 0

Now, the part {3 * (x^2) + 1} = 0 gives:

(x^2) = - (1 / 3) = (i^2) * (1 / 3)

x = ± {i * (1 / √3)}………………….both imaginary roots.

And, the part {(x^2) - 1} = 0 gives:

(x^2) = 1

x = (± 1)………………….……………………both real roots.

Answer 2

3x⁴ + 2x² - 6 - (4x⁴ - 2x² - 6)​

= 3x⁴ + 2x² - 6 - 4x⁴ + 2x² + 6

= (3 - 4)x⁴ + (2 + 2)x² + (-6 + 6)

= -x⁴ + 4x²