Algebra

AdvancedMaths revision

Quadratic Equations (Advanced)

Use discriminants, parameter conditions and root relations to analyse whole families of quadratics.

Open calculator

Focus points

✓Use discriminants with parameters.

✓Exploit root relationships.

✓Form and transform quadratic equations.

orin

Orin

The Wise Owl

Guides study flow, revision planning, and calmer focus sessions.

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 · quadratic formula

Solve 5x²−6x−2=0 exactly.

Question 2FluencyCore

Original practice · Free Online Revision

Skill · parameter discriminant

Find k so x²+kx+16=0 has equal roots.

Question 3FluencyCore

Original practice · Free Online Revision

Skill · parameter discriminant

For what values of m does x²−4x+m=0 have two distinct real roots?

Question 4FluencyCore

Original practice · Free Online Revision

Skill · root relations

If α and β are roots of 2x²−7x+3=0, find 1/α + 1/β.

Question 5FluencyCore

Original practice · Free Online Revision

Skill · forming equation

Form a quadratic with roots 2+√3 and 2−√3.

Question 6ApplicationCore

Original practice · Free Online Revision

Skill · tangency

A parabola y=x²−6x+k just touches the x-axis. Find k and the touching point.

Question 7ReasoningStretch

Original practice · Free Online Revision

Skill · root reasoning

The roots of x²−px+q=0 differ by 6 and have sum 10. Find p and q.

Question 8ChallengeStretch

Original practice · Free Online Revision

Skill · root transformation

If f(x)=x²−4x−1, find a quadratic whose roots are each 2 greater than the roots of f.