Question

For what value of \( k \) will the equation \( kx(x-2) + 6 = 0 \) have equal roots?

Hint:

Irrational Proofs: Show that the given number has a term involving an irrational number.

Answer 1

Expanding: \[ kx^2 - 2kx + 6 = 0 \] For equal roots:
\[ D = 0 \] \[ (-2k)^2 - 4(k)(6) = 0 \] \[ 4k^2 - 24k = 0 \] \[ 4k(k - 6) = 0 \] \[ k = 0 \quad \text{or} \quad k = 6 \] Thus, \( k = 6 \) ensures equal roots.
Correct Answer: \( k = 6 \)