If x=2 and x=3 are solution of the equation 3x 2 -2mx+2n=0,then find the value of m and n.
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3x²-2mx+2n = 0
2 is the solution of the equation
3(2)²-2m(2) + 2n = 0
12 - 4m + 2n = 0
4m - 2n = 12 ----------(1)
3 is another solution of the equation
3(3)²-2m(3) + 2n = 0
27 - 6m + 2n = 0
6m - 2n = 27 ---------(2)
Subtracting equation (1) from the equation (2)
6m - 2n = 27
4m - 2n = 12
-----------------
2m = 15
m = 7.5
Substitute m = 7.5 in equation (1)
4(7.5) - 2n = 12
30 - 2n = 12
2n = 18
n = 9
2 is the solution of the equation
3(2)²-2m(2) + 2n = 0
12 - 4m + 2n = 0
4m - 2n = 12 ----------(1)
3 is another solution of the equation
3(3)²-2m(3) + 2n = 0
27 - 6m + 2n = 0
6m - 2n = 27 ---------(2)
Subtracting equation (1) from the equation (2)
6m - 2n = 27
4m - 2n = 12
-----------------
2m = 15
m = 7.5
Substitute m = 7.5 in equation (1)
4(7.5) - 2n = 12
30 - 2n = 12
2n = 18
n = 9
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