 Hello and welcome to the T-Session. Today I am here to help you with polynomials. Let us discuss the following question. If the zeroes of the polynomial x cube minus 3x square plus x plus 1 are a minus b comma a comma a plus b find a and b. Now let us write the key idea first we will be using in the question. Alpha, beta, gamma are the zeroes of the polynomial. If x is equal to ax cube plus bx square plus cx plus b then alpha plus beta plus gamma is equal to minus b by a comma alpha beta plus beta gamma plus gamma alpha is equal to c by a and alpha beta gamma is equal to minus b by a. Now let us write our solution given to us the polynomial p of x is equal to x cube minus 3x square plus x plus 1 and given zeroes of p of x are a minus b a a plus b to find a and b plus d equal to 1 v is equal to minus 3 c is equal to equal to 1 equal to a minus b beta is equal to a gamma is equal to a plus b. Therefore by key idea we have now alpha plus beta plus gamma is equal to minus b by a which can be written as coefficient of x square by coefficient of beta gamma is equal to minus d by a which can be written as coefficient of x cube alpha beta gamma and d and a from the upper polynomial we get b square is equal to minus 1 which implies a cube substituting a is equal to 1 we get 1 minus b square is equal to minus 1 which implies minus b square is equal to minus 1 minus 1 which implies minus b square is equal to minus 2 this gets cut off so we are left with b is equal to root 2 so it is root value so it will be plus minus. Therefore we get a is equal to 1 and b is equal to plus minus root 2. I hope you understood the problem bye and have a good day.