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studyAlgebra
CoreMaths revision

Quadratic Equations

Solve quadratics using factorisation, completing the square and the quadratic formula.

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Focus points
✓Choose an efficient solution method.
✓Use the discriminant to classify roots.
✓Model quadratic situations.
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The Wise Owl

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target Practice set

Question lineup

Try each question first, reveal a hint when you need one, then check the worked answer. Mark them done as you go — finish the set to claim your chips.

8 revision questions
Question 1FluencyCore
Original practice · Free Online Revision
Skill · factorisation
Solve x²−7x+12=0.
Question 2FluencyCore
Original practice · Free Online Revision
Skill · factorisation
Solve 2x²−5x−3=0.
Question 3FluencyCore
Original practice · Free Online Revision
Skill · completing square
Solve x²+6x−2=0 by completing the square.
Question 4FluencyCore
Original practice · Free Online Revision
Skill · quadratic formula
Use the quadratic formula to solve 3x²+2x−7=0.
Question 5ReasoningCore
Original practice · Free Online Revision
Skill · discriminant
How many real roots does 4x²−4x+5=0 have?
Question 6ApplicationCore
Original practice · Free Online Revision
Skill · quadratic modelling
A rectangle has area 60 cm² and length 7 cm more than width. Find its dimensions.
Question 7ReasoningStretch
Original practice · Free Online Revision
Skill · repeated root
Find k so that x²−6x+k=0 has exactly one real root.
Question 8ChallengeStretch
Original practice · Free Online Revision
Skill · root relations
The roots of x²−5x−2=0 are α and β. Without solving the quadratic, find α²+β².