The problem asks us to find the value of $k$ for the quadratic equation $kx^2 - 4x + 1 = 0$ such that the roots are real and equal.

1. Problem Description

The problem asks us to find the value of $k$ for the quadratic equation $kx^2 - 4x + 1 = 0$ such that the roots are real and equal.

2. Solution Steps

For a quadratic equation of the form $ax^2 + bx + c = 0$ to have real and equal roots, the discriminant must be equal to zero. The discriminant is given by:

$D = b^2 - 4ac$

In our case, the quadratic equation is $kx^2 - 4x + 1 = 0$, so $a = k$, $b = -4$, and $c = 1$.

We need to set the discriminant to zero:

$(-4)^2 - 4(k)(1) = 0$

$16 - 4k = 0$

$4k = 16$

$k = \frac{16}{4}$

$k = 4$

3. Final Answer

The value of $k$ is 4.