If x=2 and x=3 are roots of the equation 3x2+2kx-2m . . .

Question : If x=2 and x=3 are roots of the equation 3x²+2kx-2m=0, then find the value of k and m. 

Doubt by Pushkar

Solution :
3x²+2kx-2m=0

Here 

a = 3

b = 2k

c = -2m

α=2 & β=3 (Given)

Sum of Zeroes

α+β=-b/a
2+3=-(2k)/3
5×3=-2k
15=-2k
15/(2) = -k
-15/2 = k
k=-15/2

Product of zeroes

αβ=c/a
(2)(3) = -2m/3
6 = -2m/3
(6×3)/2=-m
9=-m
-9=m
m=-9

Hence, k=-15/2 & m=-9