 Welcome to the session. In this session we will learn about the quadratic formula. Consider the quadratic equation ax square plus bx plus c equal to 0 when a is not equal to 0. Then the roots of this quadratic equation are given by minus b plus minus under root b square minus 4ac upon 2a where we have b square minus 4ac is greater than equal to 0. This formula for finding the roots of the equation is called the quadratic formula. Like if you consider the quadratic equation this here we have a is equal to 2, v is equal to 1 and c is equal to minus 6. Now let's find out what is b square minus 4ac. Now this is greater than equal to 0 so the roots of this equation are given by minus b plus minus under root b square minus 4ac upon 2a and this is equal to minus 1 plus minus 7 upon 4 that is we get two roots so these are the two roots of the equation. Now we shall discuss about the nature of roots. Again we consider the quadratic equation ax square plus bx plus c equal to 0 where a is not equal to 0. Now let's see what is the discriminant of the equation. Let it be denoted by d this is equal to b square minus 4ac. This discriminant help us determine whether the quadratic equation has real roots or not. If we have that the discriminant d that is b square minus 4ac is greater than 0 then the quadratic equation will have two distinct real roots which are given by minus b plus minus under root b square minus 4ac upon 2a. Now for this equation let's try and find out what is b square minus 4ac. This comes out to be equal to 12 which is greater than 0 so this equation has two distinct real roots which are given by minus b plus minus under root b square minus 4ac upon 2a. So these are the two roots of this quadratic equation where we get the discriminant is greater than 0. When we have the discriminant b square minus 4ac is equal to 0 then the quadratic equation would have two equal real roots which are given by minus b by 2a that is both the roots would be minus b by 2a. Consider this equation here we should find out what is b square minus 4ac. This comes out to be equal to 0. So we say that this quadratic equation has two equal real roots which are given by minus b by 2a that is the two roots are equal. Next we have if the discriminant b square minus 4ac is less than 0 then the quadratic equation will have no real roots. For the equation this we find out what is b square minus 4ac this is less than 0. So this quadratic equation would have no real roots. So this shows that when we are given a quadratic equation if we find out the discriminant of that equation we can easily make out if that equation would have real roots or not. So this completes the session hope you understood the quadratic formula and the nature of the roots.