 Hello and welcome to the session. In this session we discuss the following question which says find a cubic polynomial whose zeros are 2, 3, 4. Now a cubic polynomial whose zeros are alpha beta and gamma is given by px is equal to x cube minus alpha plus beta plus gamma x square plus alpha beta plus beta gamma plus gamma alpha into x minus alpha beta gamma. So when we are given that the zeros are alpha beta and gamma of a cubic polynomial then that cubic polynomial is equal to x cube minus alpha plus beta plus gamma into x square plus alpha beta plus beta gamma plus gamma alpha this whole into x minus alpha beta gamma. So this is our key idea that would be used in the solution for this question. Now we proceed with its solution. Now it is given that the zeros of a cubic polynomial are 2, 3 and 4 as given in the question. Now we need to find this cubic polynomial. So for this first we take let alpha be equal to 2, beta be equal to 3 and gamma be equal to 4 thus we have that alpha beta and gamma are the zeros of the cubic polynomial. Now next we find out alpha plus beta plus gamma this is equal to 2 plus 3 plus 4 equal to 9 then alpha beta plus beta gamma alpha would be equal to 2 into 3 plus 3 into 4 plus 4 into 2 that is we have put the values for alpha, beta and gamma. So this is equal to 6 plus 12 plus 8 equal to 26 thus we get alpha beta plus beta gamma plus gamma alpha is equal to 26. Next we need to find alpha beta gamma alpha beta gamma is equal to 2 into 3 into 4 and this is equal to 24 thus we have got the values for alpha plus beta plus gamma alpha beta plus beta gamma plus gamma alpha and alpha beta gamma. So the required cubic polynomial is given by say px and this would be equal to x cube minus alpha plus beta plus gamma into x square now alpha plus beta plus gamma is equal to 9 so x cube minus 9 into x square then we have plus alpha beta plus beta gamma plus gamma alpha and this whole into x so this plus 26 into x then minus alpha beta gamma so minus 24 thus px equal to x cube minus 9 x square plus 26 x minus 24 is the cubic polynomial with 0s 2 3 4. So with this we complete the session hope you have understood the solution for this question.