CAIE A-Level Mathematics 1.1.2 Quadratic Discriminant

CAIE A-Level Mathematics 1.1.2 Quadratic Discriminant
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise forming b² − 4ac after rearranging to quadratic form and solving parameter inequalities for two distinct, one repeated or no real roots.

How this is tested

  • rearrange to ax² + bx + c = 0 before identifying the correct coefficients
  • set b² − 4ac above, equal to or below zero for the stated number of real roots
  • solve the resulting parameter inequality with correct strict endpoints and interval notation

Question 1

[Maximum number: 4]

Find the set of values of the constant k for which the quadratic equation

3kx2+(k+8)x+3=03 k x^{2}+(k+8) x+3=0

has two distinct real roots.