IB DP Maths: AA HL复习笔记2.2.5 Discriminants

What is the discriminant of a quadratic function?

• The discriminant of a quadratic is denoted by the Greek letter Δ (upper case delta)
• For the quadratic function the discriminant is given by
  • • This is given in the formula booklet
• The discriminant is the expression that is square rooted in the quadratic formula

How does the discriminant of a quadratic function affect its graph and roots?

Forming equations and inequalities using the discriminant

• Often at least one of the coefficients of a quadratic is unknown
  • Questions usually use the letter k for the unknown constant
• You will be given a fact about the quadratic such as:
  • The number of solutions of the equation
  • The number of roots of the graph
• To find the value or range of values of k
  • Find an expression for the discriminant
  • Decide whether Δ > 0, Δ = 0 or Δ < 0
    • If the question says there are real roots but does not specify how many then use Δ ≥ 0
  • Solve the resulting equation or inequality