Equations and Inequalities

• Conditions for a quadratic equation to have:

(i) two real roots

(ii) two equal roots

(iii) no real roots

and related conditions for a given line to:

(i) intersect a given curve

(ii) be a tangent to a given curve

(iii) not intersect a given curve

• Solving simultaneous equations in two variables by substitution, with one of the equations being a linear equation

• Solving quadratic inequalities, and representing the solution on the number line

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