Question

Find the interval containing the solution to the following equation X^3+4.001x^2+4.002x+1.101=0

Answer 1

start by evaluating the equation at -2, -1, 0, 1, 2

if you see a sign change, then by 'intermediate value theorem' you found a solution in that range.

Answer 2

for ex :-
f(0) = 1.101
f(1) = 10.something
f(2) = postive

so there are may not be any solutions for x >= 0 !

Answer 3

similarly evaluate the euqation for x = -1, -2 .... and see if u get a sign change

Answer 4

by numerical solving
roots are
x=-0.470064
x=-0.8853
x=-2.0456
so it is sufficient to get interval around them