SOLUTION: Find all real zeros of the functions. {{{ g(x)=x^4-5x^3+7x^2+3x-10 }}}

Question 626496: Find all real zeros of the functions.

Found 2 solutions by Alan3354, jim_thompson5910:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all real zeros of the functions.

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Try the factors of 10, plus and minus.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Any rational zero can be found through this equation

where p and q are the factors of the last and first coefficients

So let's list the factors of 10 (the last coefficient):

Now let's list the factors of 1 (the first coefficient):

Now let's divide each factor of the last coefficient by each factor of the first coefficient

Now simplify

These are all the distinct rational zeros of the function that could occur

I'll let you test them all.

To test them, either use synthetic division or plug in the value into the function.

If the result is zero, then it's a root.

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