Quadratic Equations: Find Integral Values of 'k' for 2 Rational Solutions

[ritwik06]

Homework Statement

Find the number of integral values of 'k' for which the quadratic equation 2x^2 +kx - 4=0 will have two rational solutions.

Homework Equations

d=(b^2- 4ac)^(1/2)

The Attempt at a Solution

If discriminant is a perfect square, then the roots will be rational and unequal. but for how many values of 'k' starting from 2 itself will I check th discriminant to be a perfect square?

 

[Dick]

The discriminant is k^2+32. So k^2+32=n^2 where n is an integer. n^2-k^2=32. But n^2-k^2=(n-k)*(n+k). How high do you need to check?

 

[kamerling]

n is at least k+1, so n^2-k^2 >= (k+1)^2 - k^2 = 2k + 1