3. Equations and Inequalities

iGCSE (2021 Edition)

Lesson

Up to this point we have looked at many different ways to solve quadratic equations. A range of these methods are *algebraic*, meaning we focus on manipulation of the algebraic equation to find the solutions.

If the quadratic equation is simple enough we may be able to find the solution by *graphing* the function of the quadratic. However, even with simple quadratics it can be difficult to be consistent and neat enough when graphing by hand to read off the vertex and intercepts of a parabola.

Luckily, there are many forms of technology available today that can help us to solve equations both algebraically *and* graphically. The great thing about using computers when exploring mathematics is that, once we understand and are confident with the concepts, we can let them do all the heavy lifting!

Solve the following equation by using the solve command on your calculator. Write all solutions together on the same line, separated by commas.

$3x^2-x-10=0$3`x`2−`x`−10=0

Use the solve command on your calculator to find the roots of $4.6x^2+7.3x-3.7=0$4.6`x`2+7.3`x`−3.7=0.

Give your answers as decimal approximations to the nearest tenth. Write the decimal approximations for both roots on the same line, separated by a comma.

We want to solve the equation $2x\left(x-\frac{5}{2}\right)=3$2`x`(`x`−52)=3.

Rewrite the left side of the equation as a function.

Rewrite the right side of the equation as a function.

Graph both functions using the graphing functionality of your graphics calculator. Hence, solve the equation $2x\left(x-\frac{5}{2}\right)=3$2

`x`(`x`−52)=3 for $x$`x`.Write all solutions together on the same line, separated by commas.

Solve quadratic equations for real roots.