Multiple choice

If the roots of the equation $2x^{2} + k = 8x$ are real, find the range of values of $k$.

  1. $k \leq 8$
  2. $k \geq 8$
  3. $k \geq 4$
  4. $k \leq -8$
  5. $k \geq -8$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The equation is 2x^2 - 8x + k = 0. For real roots, the discriminant D = b^2 - 4ac >= 0. (-8)^2 - 4(2)(k) >= 0, so 64 - 8k >= 0, which means 8k <= 64, or k <= 8.

AI explanation

Rewrite the equation into the standard quadratic form as 2x^2 - 8x + k = 0. For the roots to be real, the discriminant must be greater than or equal to zero, so b^2 - 4ac >= 0. Substituting the values gives (-8)^2 - 4(2)(k) >= 0, which simplifies to 64 - 8k >= 0, meaning 8k <= 64 and k <= 8.

Keep practicing — related questions