CAIE A-Level Mathematics 3.9.3 The result that

CAIE A-Level Mathematics 3.9.3 The result that
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using conjugate root pairs in real-coefficient polynomial equations to find missing roots, factors and coefficient values.

How this is tested

  • state the conjugate root when a non-real root of a real polynomial is given
  • build a real quadratic factor from conjugate roots before finding remaining roots
  • use sums and products of conjugate roots to calculate real coefficients

Question 4(b)

[Maximum number: 3]

z=3e14πiz=3 \mathrm{e}^{\frac{1}{4} \pi \mathrm{i}} is a root of the equation z2+bz+c=0z^{2}+b z+c=0, where b and c are real.

State the other root and hence find the values of b and c.