Question

Solve this question with explanation please​

Answer 1

Answer:

$k = 22.5 \\ m = 63$

Step-by-step explanation:

Here: x=-2,-3

Keeping x=-2

${3x}^{2} - 2kx + 2m = 0 \\ = > {(3 \times - 2)}^{2} - (2 \times - 2)k + 2m = 0 \\ = > {( - 6)}^{2} + 4k + 2m = 0\\ = > 36 + 4k + 2m = 0 \\ let \: it \: be \: eqution \: 1$

Keeping x=-3

$= > {(3 \times - 3)}^{2} - (2 \times - 3)k + 2m = 0 \\ = > {( - 9)}^{2} + 6k + 2m = 0 \\ = > 81 + 6k + 2m = 0 \\ let \: it \: be \: eqution \: 2$

Subtracting eqution 1 from 2

$81 - 36 + 6k - 4k + 2m - 2m = 0\\ = > 45 + 2k = 0 \\ = > 2k = - 45 \\ = > k = \frac{ - 45}{2 } \\ = > k = - 22.5$

Keeping value of k in equation 1

$36 + 4k + 2m = 0 \\ = > 36 + (4 \times 22.5) + 2m = 0 \\ = > 36 +90 + 2m = 0 \\ = > 2m = - 126 \\ = > m = \frac{ - 126}{2} \\ = > m = - 63$