CAIE A-Level Mathematics 1.1.5 Equations in Quadratic Form

CAIE A-Level Mathematics 1.1.5 Equations in Quadratic Form
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise recognising repeated powers or functions as one variable, solving the resulting quadratic and converting only admissible values back to the original variable.

How this is tested

  • substitute u for a repeated power, radical or function and form a three-term quadratic
  • solve for u by factorisation or the formula before returning to the original variable
  • reject impossible intermediate values and include every real positive, negative or paired root

Question 1(b)

[Maximum number: 3]

Hence find the exact solutions of the equation 3x4−12x2−15=03 x^{4}-12 x^{2}-15=0.