discriminant

A-Maths: Find Equation of Circle Given Tangent & Circle + More

Many students after reading the question take a long time to begin as they don't know how to start. The trick is to draw! Drawing helps us to see and understand the question better.

Drawing is one of the keys to answer this question. To answer part (a), we need to notice the property of radius is perpendicular to tangent. Also, in part (b) of the question, we need to apply discriminant from the topic of Quadratic.

I have shared my thinking process and step-by-step solutions in the following videos.

How did you find the videos? Did they help you to understand better? Leave me your feedback in the comment section.

Part (a) URL: Click here to watch part (a) 7 minutes

Part (b) & (c) URL: Click here to watch part (b) & (c) 5 minutes.

[Video] A-Math: Quadratic Equation & Discriminant (Plus Common Mistakes & Counter Measures)

Commonly asked in school and 'O' Level Examinations, many students also commit to commonly made mistakes. Watch the video (5 minutes) and see how you can add another 3 marks easily.

Leave me your comment. I would love to hear from you.

Click here for a direct link to the video

Protected: Video Solution: GCE O Level 2008 Additional Mathematics Quadratic Equations (Subscribe and Get Password Access)

Quadratic Equation Discriminant Proving Question

I realize many students have a challenge with presenting the solution of proving question. I am going to illustrate the correct way using the following question.

Show that is always positive for all real values of x.

=> what is always +ve? the values of y not x ( x can be of any values)

=> The graph will not touch x-axis; it is "hanging" above the x-axis

=> No roots, hence discriminant is less than 0

TIPS FOR SHOWING/PROVING QUESTION

Have an end in your mind. Be clear of the underlying concepts that the question is asking you to prove. Work towards that. For example, in the question, we want to prove that the discriminant is less than 0. <== this is the end.
Sketch to have a clearer idea.

Quadratic Equation And Discriminant

Click on picture for larger view

Siginifance of Discriminant $b^2-4ac$ : Type of Discriminant Determines The Types of Roots/Solutions ( No root, 1 real root or 2 real and distinct roots)

E-Maths Note: Quadratic Equations & Graphs Series Revisit

I have discussed about Quadratic Equations and Graphs previously in Features of Quadratic Equations and Graphs , Different representations of quadratic equations and their significance

This is really an important topic for students taking E-Math (elementary math) , more so for A-Math (additional math) as well.

Be sure that you know the basic of recognizing if a given equation is quadratic, how the quadratic equation looks like, the 5 main features of a quadratic graph, the different methods to solve a quadratic equation.

For students taking A-Math, you would definitely need to know more about the discriminant, sum or product of roots.

I would be elaborating more on methods to solve a quadratic equation and tips on discriminant so be sure you follow the blog by subscribing to the feed here.