 Hello and welcome to the session. In this session we will learn about the quadratic equations. A quadratic equation in the variable x is of the form A x square plus B x plus C equal to 0 where A, B and C are real numbers and we have taken A not to be equal to 0. Consider the equation this, this is a quadratic equation. In fact any equation of the form P x equal to 0 where P x is a polynomial of degree 2 is a quadratic equation. Quadratic equations arise in several situations in the world like if we consider the situation in which the product of two consecutive positive integers is given to be 100 so we can write this in the form x plus 1 multiplied by x plus 2 is equal to 100. This can be further written as so the situation that the product of two consecutive positive integers is 100 is represented in the quadratic equation form as this. Now let us see how do we find the solution of a quadratic equation by factorization. Consider the quadratic equation A x square plus B x plus C equal to 0 where A is not equal to 0. The real number alpha is said to be the root of the quadratic equation above if we have A alpha square plus B alpha plus C equal to 0. We can also say that x equal to alpha is a solution of the quadratic equation. Also note that 0's of the quadratic polynomial A x square plus B x plus C and the roots of the quadratic equation A x square plus B x plus C equal to 0 are the same. We know that a quadratic polynomial can have at most two 0's so quadratic equation can have at most two roots. Now if we factorize A x square plus B x plus C into product of factors in this case this A is not equal to 0 then we have the roots of the quadratic equation A x square plus B x plus C equal to 0 can be found by equating each factor to 0. Let's consider the quadratic equation this. Now we should factorize this into the product of two linear factors so this becomes equal to x plus 2 multiplied by 2x minus 3. Now to find the roots of this equation we equate each of these factors equal to 0. So this gives the value for the variable x. Thus we get two roots of the given quadratic equation. So this is how we can find the solution of a quadratic equation by factorization. Next we see how do we find the solution of a quadratic equation by completing the square. Consider the quadratic equation A x square plus B x plus C equal to 0 where A is not equal to 0. Now let's see the steps for finding the solution of a quadratic equation by completing the square. Our first step would be if A is not equal to 1 then we divide each side by A. In the next step we move the constant to the right side. In the next step we complete the square divided by 2 the whole square on both sides. Then we write the left side as a square and simplify the right side. Then finally we equate and solve. Consider this quadratic equation in this case A as you can see is not equal to 1. So according to the first step we divide both the sides by this A. So we get this. Now according to the next step we move this constant to the right side. Now we add B upon 2 the whole square to both the sides. We write the left hand side as a square and simplify the right hand side. Now we get this. So the solution or the root of the equation would be equal to, so these are the two roots of the given quadratic equation. This completes the session. Hope you have understood what is a quadratic equation and the two methods to find the solution of a quadratic equation.