 The equation x square plus bx plus c equal to 0 has two distinct roots. So we are talking about a quadratic equation here with coefficient of x square equal to 1. x square plus bx plus c equal to 0. It has two different roots. Let's name the roots as pigeon and gorilla, b and g. Some of the roots that is b plus g is equal to 4 by 3 and product of these roots that is b times g is equal to 5 by 6. Find the values of b and c. So in a way we are asked to find the value of this coefficient of x, b and the constant term c. And at the same time we are given the sum of roots and the product of roots. So my intuition says that there has to be some connection, some relation between the coefficients and the sum and product of roots. Wait, first of all let me tell you what that relation is. For a general quadratic equation ax square plus bx plus c, sum of the roots is given as negative of coefficient of x that is negative of b divided by coefficient of x square that is a and product of roots is given as constant term c, constant term c divided by coefficient of x square again that is a. If you are wondering how did we get this relation? We can use quadratic formula to get the general expression for the roots of a general quadratic equation. Once we have them we can add both the roots and multiply them to get the expression as minus b by a and c by a respectively for sum of roots and product of roots. If you are still in doubt you can watch earlier videos of this unit where we have clearly explained how did we get this expression. As of now let's use this. So 4 by 3 would be equal to negative of b by a, a in our case is equal to 1 so this would be 1 so negative of b is equal to 4 by 3 on multiplying both sides by negative 1 b would be equal to negative of 4 by 3. Similarly c by a is equal to 5 by 6 in our case a is 1 so c is equal to 5 by 6 and I think we are done here.