Solving quadratics

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.