 Hello and welcome to the session. In this session we discussed the following question which says, if x equal to minus 1 upon m square and x equal to 1 upon n square are the roots of the equation ax square plus bx minus 1 equal to 0, then find the values of a and b. So, we are given one equation and we are given the roots of this equation. We have to find the values of a and b. Let's find out a solution now. The given equation is ax square plus bx minus 1 equal to 0. Let this be equation 1. Then it's given that x equal to minus 1 upon m square and x equal to 1 upon n square are the roots of equation 1. So, this means that minus 1 upon n square and 1 upon n square satisfies the equation 1. So, first we will put the value of x as minus 1 upon m square in equation 1. So, putting x equal to minus 1 upon m square in equation 1, we get a into minus 1 upon m square the whole square plus b into minus 1 upon m square minus 1 equal to 0. This gives us a upon m to the power 4 minus b upon m square minus 1 equal to 0. Now, for the taking LCM on the left hand side, we get in the denominator n to the power 4. In the numerator, we have a minus b into m square minus m to the power 4. This is equal to 0. So, further we get a minus b into m square minus m to the power 4 is equal to 0. Or you can say we have m to the power 4 plus b into m square minus a is equal to 0. Now, let this be equation 2. Now, next we will put x equal to 1 upon n square in equation 1. So now, putting x equal to 1 upon n square in equation 1, we get a into 1 upon n square the whole square plus b into 1 upon n square minus 1 equal to 0. This gives us a upon n to the power 4 plus b upon n square minus 1 equal to 0. Now, taking LCM on the left hand side, we get in the denominator n to the power 4. And on the numerator, we have a plus b into n square minus n to the power 4 and this is equal to 0. So, further we would get a plus b into n square minus n to the power 4 is equal to 0. That is, we now have n to the power 4 minus b into n square minus a is equal to 0. Now, let this be equation 3. So now, we have got two equations n to the power 4 plus b into n square minus a is equal to 0 and n to the power 4 minus b into n square minus a is equal to 0. So now, this was equation 2 and this was equation 3 and we need to solve both these equations to get the values for a and b. So, subtracting equation 3 from equation 2, we get n to the power 4 plus b into n square minus a minus n to the power 4 minus b into n square minus a is equal to 0. So, we get m to the power 4 minus n to the power 4 plus b into n square plus n square minus a plus a is equal to 0. Now, plus a minus a cancels, so we get m to the power 4 minus n to the power 4 plus b into n square plus n square is equal to 0. From here, we get b into n square plus n square is equal to n to the power 4 minus m to the power 4. This further gives us b is equal to n to the power 4 minus m to the power 4 upon n square plus n square. That is, we have b is equal to n square plus n square this whole into n square minus n square and this whole upon n square plus n square. n square plus n square cancels with this n square plus n square in the numerator. So, we get b is equal to n square minus n square. So, we have now got the value for b to get the value of a. We will substitute this value of b in equation 2 or 3. So, now substituting the value of b in equation 2, we get m to the power 4 plus b that is n square minus n square into n square minus a is equal to 0. This gives us m to the power 4 plus m square n square minus m to the power 4 minus a is equal to 0. Now, m to the power 4 minus m to the power 4 cancels. So, we get a is equal to n square n square. So, we have now obtained the value of a also. Thus, we get a is equal to m square n square and b is equal to n square minus n square. So, this is our final answer. With this, we complete the session. Hope you have understood the solution of this question.