If 5 lies between the roots of the quadratic equation x2 + 2(k - 3)x + 9 = 0, find the complete solution set of k.

  1. ((- 4)/10, ∞)
  2. (- ∞, (- 4)/10)
  3. (- ∞, 4/10)
  4. (4/10, ∞)

Answer (Detailed Solution Below)

Option 2 : (- ∞, (- 4)/10)
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Detailed Solution

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Let the two roots be a and b.

Given: a < 5 < b

So, from the above diagram, we can conclude that D > 0 and F(5) < 0.

F(5) < 0

52 + 2(k - 3)5 + 9 < 0

25 + 10k – 30 + 9 < 0

10k + 4 < 0

k < (- 4)/10

So,

k ε (- ∞, (- 4)/10)
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