Find the largest integral value of k so that the roots of kx^2-2x+5+0 are imaginary.

Answer 1

I think you mean "smallest" values. For the roots to be imaginary, then using the quadratic formula, b squared minus 4 times a times c (the part under the radical in the formula) must be negative. Here, a=k, b=-2 and c=5. So:

4 - 4 x k x 5 < 0

4 - 20k < 0

4 < 20k

.2 < k

So the roots will be imaginary as long as k is greater than 0.2. If k must be an integer, then the smallest value that makes the roots imaginary is 1.