Question

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

Answer 1

Answer:

k = 3

m = 0

Step-by-step explanation:

When x = 2,

3 * 2 * 2 - 2 * k * 2 + 2m = 0

12 - 4k + 2m = 0

12 = 4k - 2m (Let it be 1st equation)

When x = 3,

3 * 3 * 2 - 2 * k * 3 + 2m = 0

18 - 6k + 2m = 0

18 = 6k - 2m (Let it be 2nd equation)

Subtracting 1st equation from 2nd equation

                      18 = 6k - 2m

                      12 = 4k - 2m

                       -        -       -

                       6 = 2k

                 or,  k = 3

Putting the value of k in 1st equation,

12 = 4 * 3 - 2m

12 = 12 - 2m

2m = 0

m = 0

Hence, the value of k is 3 and m is 0.

Answer 2

Step-by-step explanation:

$\: roots \: are \: 2 \: and \: 3 \\ \: 3 {x}^{2} - 2kx + 2m = 0 \\ a = 3 \: \: \: \: b = - 2k \: \: \: \: c = 2m \\ product \: of \: zeros \: = \frac{c}{a} \\ 2 \times 3 = \frac{2m}{3} \\ 6 \times 3 = 2m \\ \frac{18}{2} = m \\ m = 9 \\ sum \: of \: zeros \: = \frac{ - b}{a} \\ 2 + 3 = \frac{ - ( - 2k)}{3} \\ 5 \times 3 = 2k \\ k = \frac{15}{2}$