Question

Find the values of m for which equation 3x² + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.

Answer 1

Given quadratic equation is 3x² + mx + 2 = 0   ...(i)

The quadratic equation has equal roots if its discriminant is zero

`=>` D = b² – 4ac = 0

`=>` m² – 4(2)(3) = 0

`=>` m² = –24

When `m = 2sqrt(6)`, equation (i) becomes

`3x^2 + 2sqrt(6)x + 2 = 0`

`=> (sqrt(3)x + sqrt(2))^2 = 0`

`=> x = sqrt2/sqrt3`

= `-sqrt(2)/sqrt(3) xx sqrt(3)/sqrt(3)`

= `-sqrt(6)/3`

When `m = -2sqrt(6)`, equation (i) becomes

x = `-sqrt(6)/3, sqrt(6)/3`