If x=2 and x=3 are roots of the equation `3x^(2)-mx+2n=0`, then find the values of m and m.

Options

A. m =-15 and n = 9
B. m =9 and n = 15
C. m =15 and n = 9
D. m =15 and n = -9

Answer

C

Explanation

Since, x=2 is a solution of `3x^(2)-mx+2n=0`
`:.3xx(2)^(2)-mxx2+2n=0`
`implies12-2m+2n=0`
`implies-m+n=-6" "....(i)`
Again, x=3 is a solution of `3x^(2)-mx+2n=0`
`:.3xx(3)^(2)-mxx3+2n=0`
`implies27-3m+2n=0`
`implies-3m+2n=-27" ".....(ii)`
On multiplying equation (1) by 2 and subtracting from (2) we get
-m = 15 or m = 15
On substituting value of m in equation (1) we get
-15 + n=-6
`impliesn=-6+15`
`impliesn=9`
Hence, m =15 and n = 9.