Find the smallest root of the equation 5x ^ 2 – x = 0

Let’s find the value of the unknown x:

5x ^ 2 – x = 0;

Let’s take the common factor x out of the parentheses:

x * (5x – 1) = 0;

Equate each factor in the equation to 0:

x = 0 or 5x – 1 = 0;

5x = 1;

x = 1/5 = 0.2.

Thus, we see that the unknown x can have two values for which the equation is true – these are 0 and 0.2. Since the task indicates to find the smallest root of the equation, the answer to the equation is zero.

Answer: x = 0.