Find the Value of k for Which the Roots Are Real and Equal
Solution
Given: $$3x^2-5x+2k=0$$
Here, $$a=3,\quad b=-5,\quad c=2k$$
For real and equal roots, $$D=b^2-4ac=0$$
$$(-5)^2-4(3)(2k)=0$$
$$25-24k=0$$
$$k=\frac{25}{24}$$
Answer
The value of k for which the roots are real and equal is: $$\boxed{\frac{25}{24}}$$