1.

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

Answer»

Given,

x2 + kx + 4 = 0

It’s of the form of ax+ bx + c = 0

Where, a =1, b = k, c = 4

For the given quadratic equation to have real roots D = b– 4ac ≥ 0

D = (k)2 – 4(1)(4) ≥ 0

⇒ k2 – 16 ≥ 0

⇒ k ≥ 4 and k ≤ -4

Considering the least positive value, we have

⇒ k = 4

Thus, the least value of k is 4 for the given equation to have real roots.



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