Çözüldü Solving Non-Linear Quartic Equation With Newton Raphson Method

https://i.ibb.co/xFwtqF6/NR.png
https: // www . youtube . com / watch?v=78fdU-prtG0 (solution with a calculator after 7:00)

Algebraic Solution:
First, choices A and E are eliminated because the root cannot be greater than 1.
f(x) = 16x^4 - 13 ⇒ f '(x) = 64x^3
Initial point: x0 = 1
x1 ≈ 1 - [ 16·(1^4) - 13 ] / [ 64·(1^3) ] = 63 / 64 ≈ 0.98
but since the real root should be slightly less than 0.98, it is supposed to be ∓0.95 because f(x) is an even function symmetric to the y-axis crossing the x-axis at two points that are equally distant from the origin, so based on the choices, -0.95 is the correct answer.