Question

If x=3 and x=2 are the roots of the equation 3x²-2mx+2n=0, find the value of m and n.

Answer 1

Here is your answer......
M=15/2
N=9

Answer 2

Hope u like my process
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If x = 3 is one of the root.. Then,

3x² - 2mx +2n =0

or, 3× 3² - 2 ×3m + 2n =0

or, 27 - 6m +2n =0

or, 6m = 27+2n
or, 12m = 54 + 4n----(1)

Again, x=2 is another root,
So,

3×2² - 2m×2 +2n = 0

or, 12 - 2× 2m + 2n =0

or, 36 - 12m + 6n =0---(multiplying 3)

or, 36 - (54+4n)+6n =0

or, 36 - 54 - 4n + 6n =0

or, 2n - 18 =0

or, n = 18/2 = 9

So...m = (27 +2n)/6

or, m = (27 +18)/6

or, m = 45/6 = 15/2 =7.5

Thus, m = 7.5 & n = 9

Hope this is ur required answer
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