SOLUTION: Hello, I'm being asked to find all real solutions of the following equation: {{{f(x) = 3x^5 + 7x^3 - 3x^2 + 2}}} Not sure how to get started here. I should be good to go once

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello, I'm being asked to find all real solutions of the following equation: {{{f(x) = 3x^5 + 7x^3 - 3x^2 + 2}}} Not sure how to get started here. I should be good to go once      Log On


   



Question 367395: Hello, I'm being asked to find all real solutions of the following equation:
f%28x%29+=+3x%5E5+%2B+7x%5E3+-+3x%5E2+%2B+2
Not sure how to get started here. I should be good to go once I know how to set the problem up. Thanks for any guidance you can provide!!

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Graph it to see if it has any real solutions.
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+graph%28+300%2C+300%2C+-3%2C+3%2C+-3%2C+3%2C3x%5E5%2B7x%5E3-3x%5E2%2B2%29+
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I used Newton's method,
f=3x%5E5%2B7x%5E3-3x%5E2%2B2
df%2Fdx=5x%5E4%2B21x%5E2-6x
x%5Bn%2B1%5D=x%5Bn%5D-f%28x%5Bn%5D%29%2F%28df%2Fdx%29%28x%5Bn%5D%29
I started with x%5B0%5D=-1 and within 5 iterations,
highlight%28x=-0.52899%29