If 2 and 3 are zeroes of polynomial 3x² – 2kx + 2m. Find the value of k and m.

As 2 and 3 are zeroes of equation 3x² – 2kx + 2m we will get 0 when we substitute x by 2 and 3

Let us substitute x = 2

⇒ 3(2)² – 2k(2) + 2m = 0

⇒ 12 – 4k + 2m = 0

Divide whole equation by 2

⇒ 6 – 2k + m = 0

⇒ m = 2k – 6 …(i)

Now substitute x = 3

⇒ 3(3)² – 2k(3) + 2m = 0

⇒ 27 – 6k + 2m = 0

Substitute value of m from equation (i)

⇒ 27 – 6k + 2(2k – 6) = 0

⇒ 27 – 6k + 4k – 12 = 0

⇒ 15 – 2k = 0

⇒ 2k = 15

Put value of k in (i)

⇒ m = 15 – 6

⇒ m = 9

Hence and m = 9