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Complex roots of quadratic equationsEdexcel International A Level Further Maths: Flashcards

What these 12 flashcards ask

  • What is the discriminant of az^2+bz+c=0?
  • What does b^2-4ac<0 tell you?
  • What is \sqrt{-16}?
  • State the quadratic formula.
  • Roots of z^2-6z+13=0?
  • Roots of z^2+4z+29=0?
  • How do the two complex roots of a real quadratic relate?
  • What do the two roots have in common on an Argand diagram?
  • Complete the square: z^2-4z+13.
  • Roots of z^2-4z+k=0 for k4?
  • What condition on k makes z^2+kz+13=0 have no real roots?
  • Distance between the roots p\pm qi?

Exam questions on Complex roots of quadratic equations

  1. The quadratic equation z2−6z+13=0z^2-6z+13=0.
    The equation z2+kz+13=0z^2+kz+13=0, where kk is a real constant, has no real roots. Find the range of possible values of kk.2 marks
  2. The quadratic equation z2+4z+29=0z^2+4z+29=0.
    Show that z=−2+5iz=-2+5\mathrm{i} satisfies the equation.2 marks
  3. The quadratic equation 2z2−6z+5=02z^2-6z+5=0.
    Solve the equation, giving the roots in the form p+qip+q\mathrm{i}.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).