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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
 one year ago
 one year 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
 one year ago
 one year ago

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harsimran_hs4Best ResponseYou've already chosen the best response.0
for 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
 one year ago

malibugranprix2000Best ResponseYou've already chosen the best response.0
so for b is 9.05
 one year ago

malibugranprix2000Best ResponseYou've already chosen the best response.0
oh I plugged something wrong. Is it, 18.66
 one year ago

harsimran_hs4Best ResponseYou've already chosen the best response.0
10 + sqrt(3) = 11.732 x^3 8x +11.732 = 0 for 2nd part
 one year ago

klimenkovBest 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.
 one year ago

wioBest ResponseYou've already chosen the best response.0
Basically, you want to use the intermediate value theorem.
 one year ago
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