\( \textbf{\underline{Solving Quadratic Equations}} \)

\( \textbf{\underline{Solving Quadratic Inequalities}} \)

When solving a quadratic inequality a graphical method is used to find the range of values of \(x\).

\( \textbf{\underline{Nature of Roots}} \)

\( \textbf{\underline{Solving simultaneous non-linear equations to find points of intersections}} \)

Solving simultaneous non-linear equations involved \(2\) or more equations that are non linear.

In this unit it will involve quadratic equations of the general form \(y = ax^2 + bx + c\) and a linear equation with a general form of \(y = mx + c\).

The solution of the simultaneous equation will be the point(s) of intersection between the line and the curve.

The nature of the point(s) of intersections, can be used to find unknown coefficients in the equation and is summarised in the table below:

Nature of points of intersection

Graphical representation

Line intersects with the curve at \(2\) points

The line intersects is tangent to the curve and intersects at \(1\) point

The line does not intersect the curve

Quadratic Equations and Inequalities - Quadratic Inequalities

Quadratic Equations and Inequalities - Quadratic Inequalities