Find the value of such that is not positive definite

MATHEMATICS · Subjective · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Find the value of

k

such that

y = \frac{1}{2}x^2 + (k - 2)x + k^2 + 4

is *not* positive definite. What relationship does the graph have with the

x

-axis in this case?