Given equation: 3x² - 10x + K = 0

We need to find the value of K for which the roots of the equation are reciprocal of each other.

Reciprocal of a number: The reciprocal of a number is obtained by interchanging the numerator and denominator of the number. For example, the reciprocal of 4 is 1/4.

Reciprocal of a root: If one root of a quadratic equation is a, then the reciprocal of that root is 1/a.

Reciprocal roots: If the roots of a quadratic equation are reciprocal of each other, then the product of the roots is 1.

Using the quadratic formula:
The roots of a quadratic equation in the form ax² + bx + c = 0 can be found using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Product of roots:
In our case, the quadratic equation is 3x² - 10x + K = 0.
Let the roots of the equation be a and 1/a.

The sum of the roots is given by:
a + (1/a) = -(-10)/3
a + 1/a = 10/3

The product of the roots is given by:
a * (1/a) = 1
1 = 1

Therefore, the product of the roots is 1.

Using the Vieta's formulas:
The product of the roots of a quadratic equation ax² + bx + c = 0 can also be found using Vieta's formulas:

Product of roots = c/a

Comparing the two methods:
We have the product of the roots as:
Product of roots = 1

Using Vieta's formulas, we have:
c/a = 1

Since the given equation is 3x² - 10x + K = 0, we can see that c/a = K/3.

Therefore, K/3 = 1
K = 3

Conclusion:
The value of K for which the roots of the equation 3x² - 10x + K = 0 are reciprocal of each other is K = 3.