Explain how we know that the given equation must have a root in the given interval. b)Use Newton's method to approximate the root correct to six decimal places.

a.) Find the root of x² - 1000 = 0 using Newton's law of approximation.

Solve using: a) Newton's method of approximation b) Secant Method Es = .00005 Find the positive root of x² + x-3=0

Use Newton's method to find 30 correct to four decimal places. Show your steps/work – including the function, your initial approximation (guess) xo, and every approximation that follows until you get to the desired level of precision (specifically, copy 3 or 4 (or 5) lines – as needed – from the table on your calculator to support your answer).