Newton's Method Calculator

Find roots of a quadratic function using Newton-Raphson iteration with step-by-step convergence.

f(x) = ax² + bx + c
Root Found
0
Iterations Used
0
f(root)
0
Converged?
—
Exact Roots (Quadratic)
—

Iteration Steps

Newton-Raphson Method

xn+1 = xn - f(xn) / f'(xn)

For f(x) = ax² + bx + c: f'(x) = 2ax + b

Convergence

  • Newton's method converges quadratically near a root
  • May fail if f'(x) = 0 at an iteration point
  • Choice of initial guess affects which root is found

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