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If both the roots of the quadratic equation x2 – 2kx + k2 + k – 5 = 0 are less than 5, then k lies in the interval
  • a)
    [4, 5]
  • b)
    (– ∞, 4)
  • c)
    (6, ∞)
  • d)
    (5, 6]
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If both the roots of the quadratic equation x2–2kx + k2+ k &ndas...
If both the roots of the quadratic equation x^2 - 5x + 6 = 0 are equal, then the discriminant of the equation, b^2 - 4ac, must be equal to zero.

In this case, the quadratic equation is x^2 - 5x + 6 = 0. Comparing it with the general quadratic equation ax^2 + bx + c = 0, we have a = 1, b = -5, and c = 6.

The discriminant is given by b^2 - 4ac. Substituting the values, we have (-5)^2 - 4(1)(6) = 25 - 24 = 1.

Since the discriminant is not equal to zero, the roots of the quadratic equation x^2 - 5x + 6 = 0 are not equal.
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If both the roots of the quadratic equation x2–2kx + k2+ k –5 = 0 are less than 5, then k lies in the intervala)[4, 5]b)(–∞, 4)c)(6, ∞)d)(5, 6]Correct answer is option 'B'. Can you explain this answer?
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