Math, asked by deydevobrata, 10 months ago

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

Answers

Answered by isafsafiya
2

Answer:

k= 5.7

m=11.6

Step-by-step explanation:

solution-------->

Given:-

x =2

x=3

given equation =3x²+2kx -2m =0

first \:  \: put \: x \:  = 2 \: in \: equation \\  \\ 3 {x}^{2}  + 2kx - 2m = 0 \\  \\ 3 \times  {2}^{2}  + 2 \times k \times 2 - 2m = 0 \\  \\ 12 + 4k - 3m = 0 \\  \\ 4k - 3m =  - 12  \:  \: -  -  -   -  -  -  - (1) \\  \\ now \: put \: x \:  = 3

now \:  \: multiply \: equation \: 1 \: by \: 2 \\  \\ 8k - 6m =  - 24 -  -  -  - (3) \\  \\ and \\  \\ multiply \: equation \: 2 \: by \: 3 \\  \\ 18k - 6m =  - 81  \:  \:  \:  \:   -  -  -  -  - (4) \\  \\  \\

 \:  \:  \:  \:  \: 8k - 6m =  - 24 \\  \\  -  \: 18k - 6m =  - 81 \\  \\  -  -  -  -  -  -  -  -  -  -  -  -  \\  \\ 10k = 57 \\ k =  \frac{57}{10}  \\ k = 5.7 \\  \\  \\ now \: put \: k = 5.7in \: equation1 \\  \\ 4k - 3m =  - 12 \\  \\ 4 \times 5.7 - 3m =  - 12 \\  \\ 22.8 - 3m =  - 12 \\  \\  - 3m =  - 12 - 22.8 \\  \\  - 3m =  - 34.8 \\  \\ m =  \frac{ - 34.8}{ - 3}  \\  \\ m = 11.6

now substract equation 3 and 4

3{x}^{2}  + 2kx - 2m = 0 \\  \\ 3 \times  {3}^{2}  + 2 \times k \times 3 - 2m = 0 \\  \\ 27 + 6k - 2m = 0 \\  \\ 6k - 2m =  - 27 -  -  -  -  -  - (2)

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