Last updated on Oct 23, 2026

The Discriminant (HSC SSCE Mathematics Advanced): Flashcards

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The Discriminant

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Formula for discriminant of $ax^2 + bx + c = 0$

$\Delta = b^2 - 4ac$

Nature of roots when $\Delta > 0$

Two distinct real roots

Nature of roots when $\Delta = 0$

One real repeated root

Nature of roots when $\Delta < 0$

No real roots

Type of roots when $\Delta > 0$ and is a perfect square

Rational numbers

Type of roots when $\Delta > 0$ but not a perfect square

Irrational numbers

Another name for root when $\Delta = 0$

Double root or equal root

Graph behaviour when $\Delta > 0$

Parabola crosses x-axis at two points

Graph behaviour when $\Delta = 0$

Parabola touches x-axis at one point

Graph behaviour when $\Delta < 0$

Parabola doesn't intersect x-axis

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The Discriminant (HSC SSCE Mathematics Advanced): Flashcards

Practise the cards

Formula for discriminant of ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

Nature of roots when Δ>0\Delta > 0Δ>0

Nature of roots when Δ=0\Delta = 0Δ=0

Nature of roots when Δ<0\Delta < 0Δ<0

Type of roots when Δ>0\Delta > 0Δ>0 and is a perfect square

Type of roots when Δ>0\Delta > 0Δ>0 but not a perfect square

Another name for root when Δ=0\Delta = 0Δ=0

Graph behaviour when Δ>0\Delta > 0Δ>0

Graph behaviour when Δ=0\Delta = 0Δ=0

Graph behaviour when Δ<0\Delta < 0Δ<0

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Exponential Functions

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Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Model Answers by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Transformations

Advanced Applications of Transformations

Explore HSC SSCE Mathematics Advanced Quizzes by Topics

Algebraic Techniques

Solve Equations

Introduction to Functions and Relations

Linear Functions

Quadratic and Cubic Functions

Function Properties

Functions and Relations

Trigonometry

Trigonometric Identities and Equations

Probability

Data

Introduction to Rates of Change

The Derivative

Exponential Functions

Logarithmic Functions

Formula for discriminant of $ax^2 + bx + c = 0$

Nature of roots when $\Delta > 0$

Nature of roots when $\Delta = 0$

Nature of roots when $\Delta < 0$

Type of roots when $\Delta > 0$ and is a perfect square

Type of roots when $\Delta > 0$ but not a perfect square

Another name for root when $\Delta = 0$

Graph behaviour when $\Delta > 0$

Graph behaviour when $\Delta = 0$

Graph behaviour when $\Delta < 0$