Multiple choice

If the equation $kx^{2}+4x+1=0$ has real and distinct roots, then:

  1. $k < 4$
  2. $k > 4$
  3. $k\leqslant 4$
  4. $k\geqslant 4$
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A Correct answer
Explanation

For real and distinct roots, D > 0. D = 4^2 - 4(k)(1) = 16 - 4k. 16 - 4k > 0 implies 16 > 4k, so k < 4.

AI explanation

For the quadratic equation kx^2 + 4x + 1 = 0 to have real and distinct roots, the discriminant must be greater than zero, meaning b^2 - 4ac > 0. Substituting the values gives 4^2 - 4(k)(1) > 0, which simplifies to 16 - 4k > 0. Solving this inequality yields 4k < 16, so k < 4.

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