Multiple choice

Find the least positive value of k for which the equation $x^{2} + kx + 4 = 0$ has real roots

  1. $k = 2$
  2. $k = 3$
  3. $k = 4$
  4. $k = 5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For real roots, discriminant D >= 0. D = k^2 - 4(1)(4) = k^2 - 16. k^2 - 16 >= 0 => k^2 >= 16. So k >= 4 or k <= -4. The least positive value is 4.

AI explanation

For the quadratic equation to have real roots, its discriminant must be greater than or equal to zero, giving the condition k squared minus 16 is greater than or equal to zero. This implies k squared is greater than or equal to 16, meaning k is less than or equal to negative 4 or k is greater than or equal to 4. The least positive value satisfying this condition is 4.

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