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GO Classes CS Test Series 2025 | Calculus | Topic Wise Test 3 | Question: 19

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The equation $x^{5}+x+1=0$ has a solution in the interval We check the endpoints of all the intervals:
$$
f(0)=1, \quad f(1)=3, \quad f(-1)=-1, \quad f(-2)=-33, \quad f(2)=35
$$
The only interval where the function changes sign is $[-1,0]$ and the intermediate value theorem guarantees the solution to exist there.
 

 

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