Find the least positive value of k for which the equation x² + kx + 4 = 0 has real roots.

For real roots, Discriminant ≥ 0

or , b² - 4ac ≥ 0

The above equation is x² + kx + 4 = 0
Comparing with ax² + bx + c = we obtain,
a = 1 , b = k , c = 4

Putting values in b² - 4ac ≥ 0 we get,

$= k^2 - 4 \times 1 \times 4 \ge 0 \\[0.5em] = k^2 - 16 \ge 0 \\[0.5em] \Rightarrow k^2 - 4^2 \ge 0 \\[0.5em] \Rightarrow (k - 4)(k + 4) \ge 0 \\[0.5em] \Rightarrow k \ge 4 \\[0.5em]$

Hence least positive value for which equation has real roots is 4 .