Multiple choice

If the roots of the equation $x^2+kx+1$ is factorisable into two linear factors, is ____.

  1. $k \leq 2$
  2. $k \geq -2 $
  3. Either $k \geq 2 $ or $k \leq -2$
  4. $-2 \leq k \leq 2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A quadratic equation x^2 + kx + 1 is factorisable into linear factors if its discriminant D >= 0. D = k^2 - 4(1)(1) = k^2 - 4. So k^2 - 4 >= 0, which means k^2 >= 4, so k >= 2 or k <= -2.

AI explanation

For the quadratic equation x^2 + kx + 1 = 0 to have real roots that can be factored into two linear factors, its discriminant must be greater than or equal to zero. Using the discriminant formula D = b^2 - 4ac, we get D = k^2 - 4(1)(1) = k^2 - 4. Setting k^2 - 4 >= 0 gives k^2 >= 4, which means k is either greater than or equal to 2, or less than or equal to -2.

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