Question

If `sqrt (2/3)` is a solution of equation 3x² + mx + 2 = 0, find the value of m.

Answer 1

For x = `sqrt (2/3)` to be solution of the given quadratic equation it should satisfy the equation

So, substituting x = `sqrt (2/3)` in the given equation, we get

`3(sqrt (2/3))^2 + m(sqrt (2/3)) + 2 = 0`

`\implies 3(2/3) + m(sqrt (2/3)) + 2 = 0`

`\implies m = -4 sqrt (3/2) = -2sqrt6`

∴ `m = -2sqrt6`