Can you help me with this problem?

Question

How can you find this function?
I don't have any idea.

Find all real zeros of the function to the nearest 0.001.
f(x)=x^3+3x^2-10x-1.
Thank you so much. I've appreciated it.

Answer 1

http://www.analyzemath.com/graphing_calculators/graphing_inverse.html

Answer 2

There are three real zeroes. The are very close to -5 , 0, and 2. What you need to do is use some technique such as newton's method to get closer and closer to the the real value.
For example, x lies between 1.9149 and 2.1276. This can be made more accurate by finding tha x lioes between 2.02127 and 2.07446. next we narrow it to lie between 2.06117 and 2.074468. next we get x is between 2.067819 and 2.07114. next it's 2.067819 and 2.06865.
So it looks like x= 2.068 is an answer to the nearest thousandth.

Now do the same for the area around 0 and then the area around -5.

Answer 3

You can use a method called Newton-Raphson method. Assume that the root of f(x) is x_0. You can make up any x_0 you want. The formula states that

x_(n+1)=x_n-f(x_n)/f'(x_n)

Here x_n is close to the root and x_(n+1) is even closer.

So in our example suppose x_0=1. Then you find x_1 using the above formula. Then from x_1 you find x_2. You stop when you notice that the third decimal place is not changing.

BTW the roots are approx 2.068, -.097 and -4.97.

If you haven't taken calc you won't understand this. So there is another method similar. Plot the graph approximately. Assume that one root is between two arbitrary points r_1 and r_2. Then find f(r_1) and f(r_2). If the product of f(r_1) and f(r_2) is negative then your guess is correct because it means that f(r_1) and f(r_2) are on either side of the x-axis. Then keep moving r_1 and r_2 closer to each other until the values of f(r_n) becomes close to zero.

Answer 4

f(x) = x^3 + 3x^2 - 10x -1
x = -4.9771144 . . . . there is only one root

Answer 5

x = 2.069 or x = -.097 or x = -4.971

there has to be three roots because it's a cubic equation.

Answer 6

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