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malibugranprix2000
 2 years ago
solving an equation
If f(x)=x^38x+10, show that there are values c for which f(c) equals;
a)pi
b)square root of 3
c)5,000,000
malibugranprix2000
 2 years ago
solving an equation If f(x)=x^38x+10, show that there are values c for which f(c) equals; a)pi b)square root of 3 c)5,000,000

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harsimran_hs4
 2 years ago
Best ResponseYou've already chosen the best response.0for each part proceed this way... a) pi let there be a number c such that f(c) = pi i.e x^3  8x + 10 = pi x^3 8x +10pi = 0 all you need to show is that there is at least one real root of this equation and you are done

malibugranprix2000
 2 years ago
Best ResponseYou've already chosen the best response.0so for b is 9.05

malibugranprix2000
 2 years ago
Best ResponseYou've already chosen the best response.0oh I plugged something wrong. Is it, 18.66

harsimran_hs4
 2 years ago
Best ResponseYou've already chosen the best response.010 + sqrt(3) = 11.732 x^3 8x +11.732 = 0 for 2nd part

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.0\(f(x)\) is continuous, so it can possess any value between \(f(a)\) and \(f(b)\). If you put \(a=\infty\) and \(b=\infty\), you will have, that your polynomial can possess any value from \(\mathbb R\). This is the proof.

wio
 2 years ago
Best ResponseYou've already chosen the best response.0Basically, you want to use the intermediate value theorem.
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