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
- 10:37 “So that we don't run into some problems. We wanna have X equals five and X equals minus four. All right, we can also, we can also have it before anyway, but this is what we have. If I have that, in this, in the same vein...”
- 16:04 “I have three X over two, I have five, I mean, I have two X over five. So for me, I have X squared plus, the other term of my two and five gives me 10, so I can have two in 10, five, five times three, that gives me 15 X,...”
- 06:35 “If I want to, maybe I should just bring you into this. Look at, if I have this to be a quadratic equation, as I just put on the board for you. And I have said this is also a quadratic equation. X squared minus alpha plus...”
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.
- 00:00 “Hello everyone, my name is Farahini E.C and I am your Mathematist teacher for today. The topic before us is Choretic Equation and we have the objectives here. In this case, you need to be able to identify the sum and pro...”
- 16:52 “out of it for me if I fix it this one in here look at what I'm going to have or shout instead of writing this alpha squared plus beta squared I'm going to write all these and they fix the product on it so with that is it...”
- 01:32 “This b is unknown. So how do you form Choretic Equation giving all this? How do you find the roots? When the Choretication has an equation that is not known. But it is very simple. From the principle we had the other tim...”
Factorization of Algebraic Expressions
This lesson covers the factorization of simple algebraic expressions and quadratic expressions. It includes methods for identifying factors and solving related word problems.
- 16:34 “the perfect square. So with that, I will give you a exercise to do the expansion. That's opening of bracket for the second and for the third. So I've been able to open the bracket, this means they are 2. So a minus b, a...”
- 13:16 “Then I have plus 2 into 14 is 7 and I have x squared, taking out x to the power 4, will be left with 1, 2x. Oh, beautiful. Now, this has given us a better idea on the factorization process. Which gives you wider view to...”
- 14:01 “This is where the values or the unknown has a square. That means it has a power of 2, but look at that. We have three identities in what, in quadratic, a plus a square gives a square plus 2 a b. Plus b squared. How does...”
Simplification of Algebraic Expressions
This lesson covers the definition of algebraic expressions and their components, including terms and coefficients. It explains how to identify like terms, perform arithmetic operations on similar terms, and simplify expressions by inserting or removing brackets.
- 08:47 “Now, to say further on that, I'm going to talk about coefficients. Coefficient is the number or factor that has been multiplied by the variable. In this expression, minus four x, the coefficient is minus four. In this ex...”
- 09:35 “addition operator. It's a plus sign. Without negative, it is positive. So here we have minus four x. And here, the coefficient is minus four, while this is a constant. Another example, if you have three x plus two, this...”
- 03:55 “Plus 2 is another term. A term can be a single number, positive or negative, or a variable, one or more numbers and variables that have been multiplied together, terms by terms, and are separated by addition or subtracti...”
Exponential Equations
This lesson covers the definition and properties of exponential equations. It explains how to solve exponential equations of linear form by ensuring the bases are the same. Examples are provided to illustrate the process of finding the unknown variable in these equations.
- 06:18 “two raised to power x or raised to power two. We use what we call the power law yeah. So minus six raised to power two raised to power x plus eight equals zero. So let's why equals two raised to power x. So it means wher...”
- 07:10 “Then two is common minus two is common here we have minus two into bracket y minus four equals zero. We can see that one minus four is common between these we have y minus four into y minus two or equals zero. So it mean...”
- 08:56 “of linear of quadratic form. And that of x or x is number two is for exponential equation of a linear form. So therefore we can use this the method that we use in our previous examples to solve this as a size. So thanks...”
Solving Simultaneous Linear Equations
This lesson covers how to solve simultaneous linear equations using substitution and elimination methods. It also explains how to identify linear equations and includes examples for practice.
- 00:00 “Hi everyone, I am Atolagbe Michael, your mathematics teacher. The topic today is simultaneous linear equation. At the end of today's lesson, you should be able to do the following. One, recall and identify simultaneous l...”
- 05:04 “But I will give you what? 2R minus instead of Q. That changes to what? Open bracket 8 minus 2R plus 2 equals to 0. Now, we have an equation. What we are going to have in negative outside of bracket? Be careful of negativ...”
- 04:16 “In equation 1, I have Q plus 2R equals to 8. So, I'm writing that. Don't forget that Q plus 2R. Q plus 2R equals to 8 equals to 1. From equation 1, make you the subject of the equation. Q equals to 8 minus 2R. You can ca...”
Whole Numbers and Prime Factorization
This lesson covers the expression of whole numbers and decimal numbers in standard form. It includes finding prime factors of numbers up to 200, determining the least common multiple (LCM), and finding the highest common factor (HCF). Additionally, it addresses perfect squares and square roots using
- 19:08 “by itself, that's a square, if you look at the box carefully, you can add that box carefully, you would observe that how many boxes do we have, that means, size times size of the blue, there's two sides, how many two sid...”
- 20:00 “that's four, if I have three times three, three times three, that's nine, if I have four times four, that gives me 16, now, what the perfect square, the perfect square is the number that results from multiplying a whole...”
- 21:33 “that's 49, eight rest of part two, that's 64, nine rest of part two, that's 81, and 10 rest of part two, that's 100, so if you now have 11 rest of part two that's 121, two, and 12 rest of part two, that'll be 144, so it...”