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Solving quadratic equationsAQA A-Level Maths: Flashcards

What these 13 flashcards ask

  • What is the first step in solving a quadratic by factorising?
  • If AB=0 what can you say?
  • State the quadratic formula.
  • Solve 2x^2-5x-12=0.
  • What is the sum of the roots of ax^2+bx+c=0?
  • What is the product of the roots of ax^2+bx+c=0?
  • Why is dividing both sides by x risky?
  • Solve x^2+4x-5=0 by completing the square.
  • What substitution solves x^4-13x^2+36=0?
  • What substitution solves x-7\sqrt x+10=0?
  • After solving for u, what must you do?
  • How many real solutions does x^2=-4 have?
  • Why do you reject some roots in word problems?

Exam questions on Solving quadratic equations

  1. The quadratic equation 2x2−5x−12=02x^{2}-5x-12=0.
    Hence, or otherwise, solve 2(y+1)2−5(y+1)−12=02(y+1)^2-5(y+1)-12=0.2 marks
  2. The equation x4−13x2+36=0x^{4}-13x^{2}+36=0.
    Solve the equation.2 marks
  3. The equation x−7x+10=0x-7\sqrt{x}+10=0, where x≥0x\geq0.
    Show that, with u=xu=\sqrt{x}, the equation becomes u2−7u+10=0u^2-7u+10=0, and hence find the values of xx.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).