Solving quadratics

Solve a quadratic equation with leading coefficient 1 by factorising it (including recognising differences of two squares and perfect-square trinomials), rearranging it to equal zero first if needed, and applying the zero product property, recognising that a quadratic can have zero, one, or two real solutions.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-5
New NZC (2026)
  • NZC26-P4-ALG-ER-K-Y10-01
  • NZC26-P4-ALG-ER-K-Y10-04
  • NZC26-P4-ALG-ER-P-Y10-03
  • NZC26-P4-ALG-ER-K-Y10-05

Resources

  • Dr Austin Maths - Solving Quadratics by Factorising or Formula Practice GridQuestions PDF · Answers
  • Dr Austin Maths - Quadratic Equations Revision Practice GridQuestions PDF · Answers
  • CorbettMaths on solving quadratics (co-efficient equal to 1)Questions PDF · Answers
  • Beta: Skills in Chapters 11, pg 210-214
  • Beta: Ex 11.14 to Ex 11.17, pgs 211 to 213

Terminology

  • quadratic equation
  • root
  • zero product property
  • roots
  • factors
  • solutions
  • parabola (graphical connection)
  • rearrange

Task goals

  • Solve a quadratic equation that is already given in factorised form by setting each factor equal to zero.
  • Factorise a quadratic trinomial with leading coefficient 1 and solve it using the zero product property.
  • Solve a quadratic equation written as a difference of two squares.
  • Solve a quadratic equation that is a perfect-square trinomial, recognising that it gives one repeated solution.
  • Rearrange a quadratic equation into the form (expression) = 0 before factorising and solving it.
  • Identify or explain an incorrect solution or claim about a quadratic equation's roots, or state how many real solutions an equation has.
  • Given one root of a quadratic equation, find the other root, or construct a quadratic equation from two given roots.
  • Solve a word problem, such as finding a rectangle's dimensions from its area or finding two numbers from their product, by setting up and solving a quadratic equation.

Where this fits

What leads into this objective, and where it goes next.

Before

Completing the Square

Completing the Square

Determining the Nature of the Roots of a Quadratic (Discriminant)

Determining the Nature of the Roots of a Quadratic (Discriminant)

Complex Roots of Polynomials

Complex Roots of Polynomials

You are here

Solving quadratics

Solving quadratics

Know

Finding square roots of numbers and solving quadratic equations are related but have some differences.

Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-01
Know

There are 0, 1, or 2 real-number solutions to x^2 = a, where a is a number.

Statement▸
Year 10 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-K-Y10-04

Next

Determining the Nature of the Roots of a Quadratic (Discriminant)

Determining the Nature of the Roots of a Quadratic (Discriminant)

Powers & Roots

Powers & Roots

Surds -- simplifying, multiplying, dividing, and adding/subtracting

Surds -- simplifying, multiplying, dividing, and adding/subtracting

Also under NA6-5:

Explore the whole sequence →

For teachers

Need the fuller teaching notes for this objective? Open the Teacher guidance PDF.