For what values of k does 2x² − kx + k = 0 have equal roots?

Correct answer: 0, 8. Equal roots need b² − 4ac = 0, so k² − 8k = 0, i.e. k(k − 8) = 0, giving k = 0 or k = 8.

Background: A quadratic has equal roots when its discriminant is zero.

• 0, 2: k = 2 does not make the discriminant zero.
• 0, −8: k = −8 does not make the discriminant zero.
• 2, 6: k = 2 or 6 does not make the discriminant zero.

Did you know? For k = 0 the equation becomes 2x² = 0.

Memory trick: Equal roots → D = 0.