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...”
- 05:08 “It becomes clearer. I remember very well that the value of alpha is actually -1/2 okay. If that is taken you can go ahead and substitute quite well for the value of alpha and for me I can go on substituting for the value...”
- 09:14 “B so that gives us a B equals -2. So a very quick one again is that we shall now go ahead and find what's the value of this expression will be okay. Look at this expression it says if you find find 1/r4 -1/b everything s...”
Radioactivity and Its Types
This lesson covers the definition of radioactivity and the characteristics of radioactive elements. It explains the three types of radiation: alpha particles, beta particles, and gamma rays, along with their properties. The lesson also includes the concept of half-life and decay constants.
- 04:05 “electrical in neutral. That is they have no charge. They have negligible mass. They have high penetrating power in A and solid and several meters in lead. They are not deflected by magnetic field. This is because they ha...”
- 04:55 “the beta particle and gamma rays. You can see that the beta particle is strongly deflected. Alpha particle is slightly deflected and the gamma ray, if you look at the gamma ray, there is no any deflection. Now I want to...”
- 02:29 “That is anytime an alpha particle is emitted from a radioactive element. Then that means an atom of helium has been emitted and helium nuclei usually represented by 4 to H e. They are relatively I mass. They have little...”
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
- 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...”
- 24:13 “that gives me x squared minus alpha plus beta x plus alpha beta equals zero. When I have this, quickly I can now see what to do with this. That means my sum is equal to minus alpha plus beta equals to minus one over thre...”
- 01:42 “And in our process, I can write X minus alpha equal zero. I can also write X minus beta equal zero. Recall that for roots of a quadratic equation, you can either have one of the factors being equal to zero or both are ze...”