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Question
If x = 2 and x = 3 are roots of the equation 3x² – 2kx + 2m = 0. Find the values of k and m.
Solution
x = 2 is a root of given equation
substitute x = 2 in L.H.S.
L.H.S. = 3(2)2 - 2k x 2 + 2m = 0
12 - 4k + 2m = 0
4k - 2m = 12 ...(i)
Similarly when x = 2 is root of given equation
Substitute x = 3 in L.H.S.
L.H.S. = 3(3)2 - 2k x 3 + 2m = 0
27 - 6k + 2m = 0
6k - 2m = 27 ...(ii)
On solving equation (i) and (ii), we get
k = `(15)/(2)` and m = 9.
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