Help me with this please..Newton-Raphson Method

Question

anonymous · Answer

An algorithmic method for constructing a sequence of approximations to a root of an equation. Suppose it is desired to solve the equation f(x)=0 and that x1 is an approximate value for the root of the equation. If we write f′(xn) for the value of the derivative of f(x) (with respect to x) evaluated at the point x=xn, the sequence defined by

$$n^{X}+1=n ^{X} - \frac{ f(n ^{X)} }{ f'(n ^{X}) }$$

usually converges to a root of the equation. It is based on constructing the tangent to the curve y=f(x) at the point (xn, f(xn)), and taking xn+1 to be the x-coordinate of the point where this tangent cuts the x-axis.

anonymous · Answer

For better understanding refer to newtons approximation of roots.

kaiz122 · Answer

$$\frac{3}{4} \tan \theta- 0.7\sin^{2}+\frac{1}{2}=0$$ at least three roots..
$$x^{3}+5x^{2}-2=0$$

can you please explain how?