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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 ax2 + bx + c = 0 Where, a =1, b = k, c = 4 For the given quadratic equation to have real roots D = b2 – 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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