Private: CAIE Alevel Pure Maths 1 (AS)

Table of Contents


find the discriminant of a quadratic polynomial ax^2+ bx + c and use the discriminant

  • e.g. to determine the number of real roots of the equation ax^2 + bx + c = 0. Knowledge of the term ‘repeated root’ is included.


  • The discriminant of a quadratic equation is a value calculated from the coefficients of the equation that provides information about the nature of the roots (or solutions) of the equation.
\Delta = b^2 - 4ac

  • The value of the discriminant determines the number of real roots of the equation and their type. Specifically:
    • If the discriminant is positive, the equation has two real roots that are distinct and different.
    • If the discriminant is zero, the equation has exactly one real root that is a repeated root.
    • If the discriminant is negative, the equation has two complex roots that are conjugates of each other.
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