How do I use the intermediate value theorem to determine whether x5+3x2−1=0 has a solution...

maduregimc

maduregimc

Answered

2021-12-17

How do I use the intermediate value theorem to determine whether x5+3x21=0 has a solution over the interval [0,3]?

Answer & Explanation

Nadine Salcido

Nadine Salcido

Expert

2021-12-18Added 34 answers

Explanation:
Bolzanos
Joseph Lewis

Joseph Lewis

Expert

2021-12-19Added 43 answers

Explanation: 
According to the intermediate value theorem:
If the function f(x) is continuous on the interval [a,b] and y is a number between f(a)  and  f(b), then there exists a number x=c in the open interval (a,b) such that y=f(c)
Here, 
f(x)=x5+3x21 
is a continouos function on the interval [0,3] as f(x) is a polynomial function. 
f(0)=1 
f(3)=243+271=269 
0(f(0),f(3)) 
As f(x) changes sign from f(0) as f(3) 
c(0,3) such that f(c)=0 
The intermediate value theorem is used in this situation.

RizerMix

RizerMix

Expert

2021-12-29Added 437 answers

The guys above, they decided everything for sure, I will not repeat myself and I will not write another one from

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