If roots of `4x ^(2) - 2x +c =0` are reciprocal of each other then the value of c is `"________".`

Answer

To find the value of \( c \) in the quadratic equation \( 4x^2 - 2x + c = 0 \) given that the roots are reciprocal of each other, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the quadratic equation**:
The given quadratic equation is \( 4x^2 - 2x + c = 0 \).

2. **Recall the property of roots**:
For a quadratic equation \( ax^2 + bx + c = 0 \), the product of the roots \( r_1 \) and \( r_2 \) is given by the formula:
\[ r_1 \cdot r_2 = \frac{c}{a} \]
where \( a \) is the coefficient of \( x^2 \) and \( c \) is the constant term.

3. **Set up the relationship for reciprocal roots**:
If the roots are reciprocal, we can denote the roots as \( r_1 = x \) and \( r_2 = \frac{1}{x} \). Therefore, the product of the roots can be expressed as:
\[ r_1 \cdot r_2 = x \cdot \frac{1}{x} = 1 \]

4. **Substitute into the product formula**:
From the property of the product of the roots, we have:
\[ 1 = \frac{c}{4} \]
Here, \( a = 4 \) (the coefficient of \( x^2 \)).

5. **Solve for \( c \)**:
To find \( c \), we can rearrange the equation:
\[ c = 4 \cdot 1 = 4 \]

6. **Conclusion**:
Thus, the value of \( c \) is \( 4 \).

### Final Answer:
The value of \( c \) is \( \boxed{4} \).