Question

if x=2 and x=3 are roots of the equation 3x square -2mx+2n:find the value of m and n

Answer 1

Hiii friend,

X = 2

P(X) = 3X²-2MX+2N

P(2) = 3 × (2)² - 2 × M × 2 + 2N

=> 3 × 4 - 4M + 2N

=> 12- 4M + 2N = 0

=> 4M -2N = 12........(1)

Also X = 3

Therefore,

P(3) = 3 × (3)² - 2M × 3 + 2N

=> 3 × 9 - 6M + 2N

=> 27 - 6M + 2N = 0

=> 6M -2N = 27......(2)

From equation (1) we get,

4M -2N = 12

4M = 12+2N

M = (12+2N/4)........(3)

Putting the value of M in equation (2)

6M - 2N = 27

6 × (12+2N/4) - 2N = 27

3(12+2N)/2 - 2N = 27

36 + 6N/2 - 2N = 27

36+6N - 4N= 27
_________
2

36 +2N = 27 × 2

36 +2N = 54

2N = 54-36

2N = 18

N = 18/2 = 9

Putting the value of N in equation (3)

M = (12+2N/4) = 12 + 2 × 9/4

M = 12+18/4 = 30/4 = 15/2

Hence,

N = 9 and M = 15/2

HOPE IT WILL HELP YOU....... :-)

Answer 2

Given that roots are 2 and 3

Taking x = 2,

=> 3x² - 2mx + 2n =0

=> 3(2)²-2(2)m + 2n = 0

=> 3(4) - 4m + 2n = 0

=> 12 - 4m + 2n = 0

=> 12 = 4m - 2n ----1equation

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Then, Taking x= 3,

=> 3x² -2mx + 2n = 0

=> 3(3)²-2(3)m + 2n =0

=> 3(9) -6m + 2n= 0

=> 27 - 6m + 2n =0

=> 27= 6m - 2n ----2equation

====================

Subtracting 2equation from 1equation

12 = 4m - 2n
27=6m - 2n
- - +
__________
-15= -2m
_________

15/2 = m

Putting the value of m in 1equation,

12 = 4(15/2) - 2n

12 = 2(15) - 2n

12 = 30 - 2n

12 -30 = -2n

18= 2n

18/2 = n

9 = n

:-)