Answer:

To find the value of k in each quadratic equation to have equal roots, we can apply the discriminant formula.

1) For the equation Kx² + 2x + 1 = 0:

The discriminant (D) formula is given by D = b² - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax² + bx + c = 0.

In this equation, a = K, b = 2, and c = 1. For the equation to have equal roots, the discriminant must be equal to zero (D = 0).

Substituting the values into the discriminant formula, we have:

0 = (2)² - 4(K)(1)

0 = 4 - 4K

To solve for K, we can rearrange the equation:

4K = 4

K = 1

So, for the equation Kx² + 2x + 1 = 0 to have equal roots, the value of k should be equal to 1.

2) For the equation 2x² + 4x + 4 = 0:

Using the same steps as above, we can identify the coefficients as a = 2, b = 4, and c = 4. Again, we want the discriminant to be equal to zero.

Substituting the values into the discriminant formula:

0 = (4)² - 4(2)(4)

0 = 16 - 32

0 = -16

Since the discriminant is negative, the equation 2x² + 4x + 4 = 0 does not have equal roots, and therefore, there is no value of k that will achieve equal roots in this equation.