Find the Value of k for Which the Roots Are Real and Equal
Solution
Given: $$kx^2-2\sqrt{5}x+4=0$$
Here, $$a=k,\quad b=-2\sqrt{5},\quad c=4$$
For real and equal roots, $$D=b^2-4ac=0$$
$$(-2\sqrt{5})^2-4(k)(4)=0$$
$$20-16k=0$$
$$k=\frac{20}{16}=\frac{5}{4}$$
Answer
The value of k for which the roots are real and equal is: $$\boxed{\frac{5}{4}}$$