Last updated on Sep 20, 2026

The Discriminant (VCE SSCE Mathematical Methods): Flashcards

The Discriminant

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$\Delta = b^2 - 4ac$

Delta ( $\Delta$ )

No real solutions

One solution (or two coincident solutions)

Two distinct real solutions

Number and type of solutions without solving

Two rational solutions

Two irrational solutions

One rational solution

Two identical solutions at the same point

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The Discriminant (VCE SSCE Mathematical Methods): Flashcards

Practise the cards

Formula for discriminant (Δ\DeltaΔ) of ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0

Greek letter representing the discriminant

Number of real solutions when Δ<0\Delta < 0Δ<0

Number of solutions when Δ=0\Delta = 0Δ=0

Number of solutions when Δ>0\Delta > 0Δ>0

What does the discriminant tell us?

Type of solutions when Δ\DeltaΔ is a perfect square (≠0\neq 0=0)

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

Type of solution when Δ=0\Delta = 0Δ=0

What are coincident solutions?

Explore VCE SSCE Mathematical Methods Revision Notes by Topics

Expanding and Collecting Like Terms

Factorising

Quadratic Equations

Graphing Quadratics

Completing the Square and Turning Points

Graphing Quadratics in Polynomial Form

Solving Quadratic Inequalities

The General Quadratic Formula

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

Explore VCE SSCE Mathematical Methods Model Answers by Topics

Expanding and Collecting Like Terms

Factorising

Quadratic Equations

Graphing Quadratics

Completing the Square and Turning Points

Graphing Quadratics in Polynomial Form

Solving Quadratic Inequalities

The General Quadratic Formula

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

Explore VCE SSCE Mathematical Methods Quizzes by Topics

Expanding and Collecting Like Terms

Factorising

Quadratic Equations

Graphing Quadratics

Completing the Square and Turning Points

Graphing Quadratics in Polynomial Form

Solving Quadratic Inequalities

The General Quadratic Formula

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

Explore VCE SSCE Mathematical Methods Exam Questions by Topics

Expanding and Collecting Like Terms

Factorising

Quadratic Equations

Graphing Quadratics

Completing the Square and Turning Points

Graphing Quadratics in Polynomial Form

Solving Quadratic Inequalities

The General Quadratic Formula

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

The Discriminant

Solving Simultaneous Linear and Quadratic Equations

Families of Quadratic Polynomial Functions

Quadratic Models

Formula for discriminant ( $\Delta$ ) of $ax^2 + bx + c = 0$

Number of real solutions when $\Delta < 0$

Number of solutions when $\Delta = 0$

Number of solutions when $\Delta > 0$

Type of solutions when $\Delta$ is a perfect square ( $\neq 0$ )

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

Type of solution when $\Delta = 0$