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  • A-Level Maths

Quadratic & Simultaneous Equations and Inequalities

The standard format of a quadratic expression is ax² + bx + c

There are three ways of solving quadratic equations:


Factorising

Factorise a quadratic in the form ax² + bx + c = 0, and set each bracket to equal 0 to find the values of x (the roots).


The Quadratic Equation

the quadratic equation, the discriminant, solving quadratic equations. EngineeringNotes.net, EngineeringNotes, Engineering Notes

The (b² - 4ac) inside the square root is known as the discriminant, and is used to show how many roots a quadratic has:

  • b² - 4ac > 0: The quadratic has two distinct roots

  • b² - 4ac = 0: The quadratic has one repeated root

  • b² - 4ac < 0: The quadratic has no real roots


Completing the Square

Completing the square, solving quadratic equations, A-Level Maths notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes

More commonly, quadratics are in their standard form. In this case, this version is used:

Completing the square, solving quadratic equations, A-Level Maths notes. EngineeringNotes.net, EngineeringNotes, Engineering Notes



Simultaneous Equations

Linear Simultaneous Equations