Roots of Quadratic Equations
This lesson covers how to find the sum and product of the roots of a quadratic equation. It also explains how to form a quadratic equation given the roots and states the conditions for equal roots, real roots, and no roots. Additionally, it discusses the relationship between a line and a curve in te
- 00:50 “of a quadratic equation. At the same time, it should be able to also form a quadratic equation if I'm giving the roots. Having said that, we like to have some introduction. If I have alpha as one of the roots, and the se...”
- 00:02 “Hi, everyone. My name is Fawahimi EC, and I'm your Math Teacher for this session. The topic we're gonna have this time around is finding the roots of a quadratic equation, and also forming a quadratic equation given the...”
- 02:27 “When I have this, I can expand. And when I just done, what happened is, you have to follow the process we had before. The X here can go to multiply the X here, and the X here can go to multiply this. In the same thing, t...”
Quadratic Equation and Roots
This lesson covers the formation of quadratic equations from given roots. It explains how to find the sum and product of the roots and demonstrates solving for unknown coefficients in a quadratic equation. Examples are provided to illustrate these concepts.
- 23:29 “48 over 6 and for you know you can get that to be 8 and if alpha cube is going to 8 so therefore your alpha is actually 2 because 2 is the cube of 8 so I mean the cube root of 8 is 2 or 2 is the cube of 8 so if alpha is...”
- 16:01 “this gives me alpha squared plus beta squared over alpha plus beta squared minus I can always take care of this because I know the value of my product to be 3 over 8 but I can still relax and fix it later on so in this c...”
- 00:46 “Having said that, we have examples we would like to treat here. Look at the question one here. If you have one of the roots alpha to be -1/2, excuse me, one of the roots is alpha and is -1/2. This question is saying that...”
Prefixes and Root Words
This lesson teaches what prefixes are and how they function in word formation. Students will learn to identify basic root words and use prefixes to create antonyms. The concept of morphemes as the smallest units of sound will also be explained.
- 00:00 “Good students, I'm Mr. Kenny. I'm your English teacher for today. This moment we are going to discuss prefixes. Both before the class commences, I would like to read the lesson objectives in your hearing. Now after the t...”
- 11:13 “Now, we have examples of prefix, examples of prefix. Number one on the list is engulf. Engulf means to be overwhelmed. Engulf means, you know, to be surrounded. That's what it means. Now, we have engulf, engulf, engulf....”
- 07:35 “up is saved and that is our stem. So that's what the saying is is stem is what remains of a word when any inflection. Inflection means attachments. That's attachments could be prefix and that attachments could be suffix....”
Roots of Quadratic Equations
The lesson covers the sum and product of the roots of quadratic equations. It explains how to form a quadratic equation given the sum and product of its roots, and states the conditions for equal roots, real roots, and no roots. The lesson also identifies conditions for a line to intersect or be tan
- 07:18 “when the sum and when the roots of the quadratic equation are given. So if, for example, you are given the roots of quadratic equation alpha, alpha plus beta, alpha, let's alpha and beta be the roots of quadratic equatio...”
- 08:04 “So that is how to find. So if, for example, in this example and about 2, if you are given, find the quadratic equation. Who's root are, or if you go 1? We have minus 1 and it's minus 1 and it's. So it means our alpha a i...”
- 01:34 “minus b plus square root of b squared minus a c all over 2a, all x equals minus b minus square root of b squared minus 4a c all over 2a. So this is the root of quadratic equation. But how do we, the sum of the sum and th...”