Find the values of k for which the quadratic equation 9x2 - 3kx + k = 0 has equal roots.
Given: Quadratic equation 9x2-3kx + k = 0 has equal roots
Let β be the equal roots of the equation
Thus 2β =(3k)/9=k/3 (Sum of the roots is equal to –b/a)
We get β=k/6 or β2=k2/36
Also that β2=k/9 (Product of the roots is equal to c/a)
For k ≠ 0,k/36=1/9