# Prove that 5x^3+4x-2=0 has exactly one solution

Prove that 5x^3+4x-2=0 has exactly one solution

## This Post Has 3 Comments

1. Expert says:

step-by-step explanation:

2. Expert says:

6xy and -16xy000000000

3. sabrinarasull1pe6s61 says:

$5x^3+4x-2=0\\\\&10;(5x^3+4x-2)'=15x^2+4\\\\&10;15x^2+4=0\\&10;15x^2=-4\\&10;x^2=-\dfrac{4}{15}\\&10;x\in\emptyset &10;$

The derivative of $5x^3+4x-2$ is positive for all real numbers, which means the function is increasing in its all domain and therefore there is only one intersection with the x-axis ⇒ one solution.