 Hello and welcome to the session. In this session, we shall discuss the topic of quadratic equations, a polynomial equation, a second degree, a quadratic equation. An equation is said to be of second degree. If an x, the variable appears to the second power, which is the highest part of the equation, ax squared plus dx plus c equal to 0, is the standard form, standard form of the quadratic equation, a, b and c are the constants and a is not equal to 0. Here is now c, what is the root of a quadratic equation? A root is the value of the variable that makes the equation true. Now since the degree of the quadratic equation is true, so a quadratic equation makes we discuss solving quadratic equations. We shall discuss three types of quadratic equations and the methods of solving those types of quadratic equations. So in type one, we have the equation of the form ax squared equal to k, where this k is some constant and if we are given an equation which can be reduced to this form also, that is also to be done in the same way as we do this equation. So for this, we divide coefficient of the square root of both numbers of the equation or we can say we take the square root on both the sides of the equation as obtained. For example, consider the equation 2x square is equal to 8. As you can see, this is of the form ax squared 2k, the coefficient of x square that is 2, so 2x squared upon 2 is equal to 8 upon 2. Now 2 cancels with 2 and 2, 4 times is 8, that is we have x square is equal to 4, square root of both the numbers of the equation and if we take square root on both the sides, so x square is equal to square root of 4 which gives us x is equal to plus minus 2. We can also check the solution of the quadratic equation values of x as plus 2 and minus 2. Now consider this equation as equation 1. Now in equation 1 into 2 square is equal to 8, that is 2 into 4 which is 8 is equal to 8, coefficient of the equation. In the same way, there is equal to 8, that is 2 into 4, that is 8 is equal to 8. This is also equation 1. Now we can check the solution of the equation. Now let's consider another type of the quadratic equation of the form ax squared equal to bx. Now when we have the equation of this type, then first we express equation of the form ax square equal to bx in the form x square minus bx is equal to 0. Then next we factorize the left hand side that is the mhs can be done by taking x common, so x into minus b the whole is equal to 0. We take each factor equal to 0, x equal to 0, x minus b is equal to 0. Each resulting is we would get x equal to 0 or solving this equation we would get x equal to b upon every equation 3x square equal to 18x. This equation is of the type equal to bx. So first of all we express this in the form of ax square minus bx is equal to 0. Thus we can write the given equation 3x square equal to 18x is equal to 0. Then next we factorize the left hand side and this can be done by taking 3x common. So 3x into x minus 60 whole is equal to 0, x we put each factor equal to 0 and here we have to factor each factor equal to 0 we get 3x equal to 0, x equal to 0, equal to 0 or x equal to 6. Now we can check each of these solutions that would give an equation for a given value of x then that value of x would be the solution of the given equation. Now before checking the solution we can say here that x is equal to 0 or x is equal to 6 after checking if we find that both 0 and 6 satisfy the given equation then we can say that 0 and 6 are the roots of the given equation. If we have the quadratic equation in the standard form as ax square plus bx plus c equal to 0 and any other equation of any form which can be reduced to this form in this form we would the left hand side square plus bx plus c and then we left factor equal to 0 which resulting equation is of x in the given equation. Here is now x minus 10 is equal to 0. So this equation is given in the standard given equation 3x square plus x minus 10 equal to 0. We first need to factorize the left hand side square plus xx minus 5x minus 10 is equal to 0. Now taking 3x we get 3x into we get minus 5 into x less to the whole equal to 0 so the whole into 3x minus 5 the whole is equal to 0. The given quadratic equation we will now let each of these factors equal to 0 so x plus 2 equal to 0 5 equal to 0 these two equations we get to the checking. Now before we do the checking we say that x equal to minus 2 or x equal to 5 upon 3 the equation x equal to minus 2 in equation 2 we get 3 into minus 2 whole square plus of minus 2 minus 10 is equal to 0 this means that 3 into 4 is equal to 0 or you can say that 0 is equal to 0. So this is nothing given quadratic equation in the same way we consider x equal to 5 upon 3 in the given equation 2 we get 3 into 5 upon 3 the whole square plus 5 upon 3 minus 10 is equal to 0 25 upon 9 upon 3 minus 10 is equal to 0. Now 3 we have 25 upon 3 plus 5 upon 3 minus 10 is equal to 0 or you can also say that 30 upon 3 minus 10 is equal to 0 and 3 10 times is 30 and 10 minus 10 is 0 is equal to 0 which is 2 and say that x equal to 5 upon 3 is also the solution of the equation. Upon 3 the equation will be understood the concept