Use the Intermediate Value Theorem to show that there is a root of equation x 3

Merati4tmjn

Merati4tmjn

Answered question

2022-04-07

Use the Intermediate Value Theorem to show that there is a root of equation
x 3 + 2 x 1 x = 0
in ( 1 4 , 1 ). Find this root to two decimal places.

Answer & Explanation

arbotsck8sg

arbotsck8sg

Beginner2022-04-08Added 22 answers

Hint for existence: if you let
f ( x ) := x 3 + 2 x 1 x ,
note that f ( 1 4 ) < 0 , f ( 1 ) > 0. Hence, ...

Hint for value: to calculate the zero, note that
x 3 + 2 x 1 x = 0 y 2 + 2 y 1 = 0 ,
if you define y := x 2 .

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