 Hello and welcome to the session. In this session we will discuss a question which says that if 1 root of AX square plus BX plus C is equal to 0 may be 4 by 3 times the other show that 12B square is equal to 49AC. Now before starting the solution of this question we should know some results. Now the standard form of quadratic equation is AX square plus BX plus C is equal to 0 where A is not equal to 0 and ABC are the constants. Now let P and Q are the roots of this equation. Then sum of the roots that is P plus Q is equal to minus B over A which means the sum of the roots is equal to minus coefficient of X over coefficient of X square in the given equation. Also product of the roots that is P into Q or PQ is equal to C over A which means product of the roots is equal to the absolute term over coefficient of X square in the given equation. Now these results will work out as a key idea for solving out this question. And now we will start with the solution. Here the equation is given as AX square plus BX plus C is equal to 0. Now here in the question it is given that one root of this equation may be 4 by 3 times the other. Let one root of the above equation is equal to alpha. Then the other root according to the given condition will be equal to 4 by 3 times this root that will be equal to 4 by 3 alpha. Now we know that sum of the roots is equal to minus B over A. So sum of the roots is equal to minus B over A. Now here the roots are alpha and 4 by 3 alpha. So therefore this implies alpha plus 4 by 3 alpha is equal to minus B over A. This implies now on taking the algorithm which is 3 it will be 3 alpha plus 4 alpha by 3 is equal to minus B over A. Which implies 3 alpha plus 4 alpha is 7 alpha by 3 is equal to minus B over A. Which implies alpha is equal to minus 3B over 7A. Now let us take this equation as equation number one. Now we know that the product of the roots is equal to C over A. So the product of the roots is equal to C over A. Now here the roots are alpha and 4 by 3 alpha. So therefore this implies alpha into 4 by 3 alpha is equal to C by A. Which implies 4 by 3 alpha square is equal to C by A. Now from one putting the value of alpha here this gives 4 by 3 into minus 3B over 7A whole square is equal to C by A. This is from one which implies 4 by 3 into minus 3B over 7A whole square is 9B over 7A whole square. 4B square over 49A square is equal to C over A. Now here 3 into 3 is 9. So this implies 4 into 3 is 12B square over 49A square is equal to C over A. Now cross multiplying this implies 12AB square is equal to 49A square C. Now dividing both sides by A. This implies 12B square is equal to 49AC. So this is the solution of the given question and that's all for this session. Hope you all have enjoyed this session.