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

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

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
It 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' ?
 one year ago

alrightatmaths Group TitleBest ResponseYou've already chosen the best response.0
Yeah, 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?
 one year ago

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

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

alrightatmaths Group TitleBest ResponseYou've already chosen the best response.0
Good man!
 one year ago
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