Question

A graphing calculator is recommended. Use Newton's method to find all solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. (Enter your answers as a comma-separated list.) -2x7 - 4x4 + 9x3 + 5 = 0 X =

plz answer

Answer 1

Writing the equation into a graphing calculator, we get the graph of the given polynomial function as

10 o -3 2 11 0 3 2 5 - 100 5

Thus, we can see from the graph that the given function has three real roots: one near -1.5, one near -0.5 and one near 1.5

Now, we use Newton-Raphson method, with these initial guesses, on the function, to get our roots:

Using the initial point x = -1.5, we get the solution as x ≈ -1.638579079601

Using the initial point x = -0.5, we get the solution as x ≈ -0.760382980974

Using the initial point x = 1.5, we get the solution as x ≈ 1.3134698020456

Thus, the roots, as a comma-separated list, are

$\small -1.63857908,\; -0.76038298,\; 1.31346980$