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

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

Sum

x² + kx + 4 = 0
Here, a = 1, b = k, c = 4
b² - 4ac
= k² - 4 x 1 x 4
= k² - 16
∵ Roots are real and positive.
∴ k² - 16 ≥ 0
⇒ k²≥ 16
⇒ k ≥ 4
⇒ k = 4.

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