Solving quadratics ax^2 + bx + c = 0 where a is not 1, by factorising

Task goals

• Solve a quadratic equation that is already given in factorised form, such as (2x + 1)(x + 3) = 0, using the zero-product property.
• Factorise a quadratic trinomial ax^2 + bx + c where a is not 1, by finding two numbers that multiply to a*c and add to b, splitting the middle term, and factorising by grouping, then solve the resulting equation.
• Rearrange a quadratic equation into the form ax^2 + bx + c = 0 before factorising and solving.
• Given one root of a factorised quadratic equation, find the other root without fully re-solving.
• Find an unknown coefficient in a quadratic equation given its two roots.
• Identify or explain an error in a student's incorrect factorisation or solution of a quadratic equation.
• Create a quadratic equation from a given pair of factors or roots, then solve it, and compare the relative difficulty of factorising two different quadratic equations.