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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Quadratic Equation

NDA 2023 · Mathematics · Quadratic Equation

For how many integral values of k , the equation x^2-4 x+k=0 ,...

For how many integral values of kk, the equation x2−4x+k=0x^2-4 x+k=0, where kk is an integer, has real roots and both of them lie in the interval (0,5)(0,5) ?

Options

  1. A33
  2. B44
  3. C55
  4. D66

Correct answer

B. 44

Step-by-step solution

x2−4x+K=0x^2-4 x+K=0 For real roots, D≥0⇒(−4)2−4(1)(K)≥016−4K≥04−K≥0K≤4D \geq 0\Rightarrow \quad(-4)^2-4(1)(K) \geq 016-4 K \geq 04-K \geq 0K \leq 4 but Both roots lie in (0,5)(0,5). K=1,2,3,4K=1,2,3,4 (integers) Number of integral values =4=4.
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