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 one year ago
f(x) = x^3 + 8x  19
Show that the equation f(x)=0 has only one real root.
 one year ago
f(x) = x^3 + 8x  19 Show that the equation f(x)=0 has only one real root.

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Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0I can only recommend the NewtonMethod or the Method of Bisection for this problem.

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1It is a polynomial of the 3rd degree. Look at the endbehaviour of the function: The limit of f(x) if x => infinity is also infinity. The limit of f(x) if x => infinity is also infinity. f is continuous for every x, so it must be 0 at least one time. Now look at the derivative: f'(x)=3x²+8. What do you know about the possible values of f' ?

alrightatmaths
 one year ago
Best ResponseYou've already chosen the best response.0Yeah, you know it has to have one because there is a change in sign basically. And are you saying that f'(x) will never be zero so there's no turning point?

alrightatmaths
 one year ago
Best ResponseYou've already chosen the best response.0Or that it's always positive.

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1That is just what I wanted to say ;) So f is always increasing...
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