For what value of 'm' and 'n' - 1 and 2 are the roots of the polynomialx3+mx2+nx+6 ?

Explanation

Solution: This question can be solved by putting the value of roots individually in the equation, this will generate two separate equations which are to be solved using the elimination method.The roots are -1 and 2.x=2 x=-1(2)3+m(2)2+n2+6=0 (-1)3+m(-1)2+n-1+6=08+4m+2n+6=0 -1+m-n+6=014+4m+2n=0 5+m-n=027+2m+n=07+2m+n=0Now we will solve these two equations simultaneously. 2m+n=-7 m-n=-5 3m = -12 m = -123= -4Put the value of m in any of the above equations to find value of n.5+m-n=05+(-4)-n=05-4-n=0-n+1=0-n=-1n=1