If one root of the quadratic equation 3y2 – ky + 8 = 0 is 2/3, then find the value of k

3. If one root of the quadratic equation 3y² – ky + 8 = 0 is 2/3,  then find the value of k.

Sol. 3y² – ky + 8 = 0

y = 2/3, is the root of given quadratic equation.

So it satisfies the given equation.

∴ 3(2/3)² – k(2/3)  + 8 = 0

∴ 3(4/9) – 2k/3 + 8 =0

∴ 12/9 – 2k/ 3 + 8 = 0

Multiplying the equation by 9 we get,

12 – 6k + 72 = 0

∴ 6k = 84

∴  k = 84/6

∴ k = 14