To solve this quartic equation, we can try to factor it or use numerical methods to find the roots.
One way to potentially factor the equation is by grouping:
X^4 - 8x^3 - 4x^2 + 16x + 4 = 0
Factor out common terms:
x^3(x - 8) - 4(x^2 - 4) + 4 = 0
(x^3 - 4)(x - 8) + 4 = 0
(x^3 - 4)(x - 8) = -4
(x^3 - 4) = -4 / (x - 8)
x^3 = -4 / (x - 8)
This factorization doesn't provide a clear way to further simplify the equation. Thus, we can use numerical methods such as the Newton-Raphson method or the Numerical Analysis method to approximate the roots of the equation, or use a computer algebra system to solve it.
To solve this quartic equation, we can try to factor it or use numerical methods to find the roots.
One way to potentially factor the equation is by grouping:
X^4 - 8x^3 - 4x^2 + 16x + 4 = 0
Factor out common terms:
x^3(x - 8) - 4(x^2 - 4) + 4 = 0
(x^3 - 4)(x - 8) + 4 = 0
(x^3 - 4)(x - 8) = -4
(x^3 - 4) = -4 / (x - 8)
x^3 = -4 / (x - 8)
This factorization doesn't provide a clear way to further simplify the equation. Thus, we can use numerical methods such as the Newton-Raphson method or the Numerical Analysis method to approximate the roots of the equation, or use a computer algebra system to solve it.