Find the Value of k for Which the Roots Are Real and Equal
Solution
Given: $$9x^2-24x+k=0$$
Here, $$a=9,\quad b=-24,\quad c=k$$
For real and equal roots, $$D=b^2-4ac=0$$
$$(-24)^2-4(9)(k)=0$$
$$576-36k=0$$
$$36k=576$$
$$k=16$$
Answer
The value of k for which the roots are real and equal is: $$\boxed{k=16}$$