Question

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

Answer 1

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

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