Respuesta :
Answer:
The answer is "4.3".
Step-by-step explanation:
Given:
[tex]\to x^3 - 5x - 59 = 0[/tex]
When [tex]x = 4.1:[/tex]
[tex]\to f(4.1) = (4.1)^3 - 5(4.1) - 59 = -10.579[/tex]
When [tex]x= 4.2:[/tex]
[tex]f(4.2) = 4.2^3 - 5(4.2) - 59 = -5.912[/tex]
When [tex]x = 4.3:[/tex]
[tex]\to f(4.3) = -0.993[/tex] (closer to 0)
[tex]\to f(4.4) = 4.184[/tex]
- It changes the sign so, the root lies in 4.3 and 4.4.
When [tex]x = 4.35:[/tex]
[tex]\to f(4.35) = 1.563[/tex]
When the root is closer to 4.3 than 4.4 So, 1.563 is closer to zero than 4.184.
When [tex]x = 4.32:[/tex]
[tex]\to f(4.32) = 0.0216[/tex] close to zero.
So the answer is 4.3 to 1 decimal place.
