Find the value of k for which the quadratic equation ( k - 2) x2 + ( 2k - 3) x + ( 5k - 6) = 0 has equal roots.

As per the question statement, roots of the equation ( k - 2) x² + ( 2k - 3) x + ( 5k - 6) = 0 are equal.

So, the value of its determinant will be equal to zero as for equal roots the determinant is always zero, i.e. b² – 4ac = 0.

In the equation ( k - 2) x² + ( 2k - 3) x + ( 5k - 6) = 0,

a = ( k - 2) , b = 2( 2k - 3) , c = 5k - 6

Now, equating its determinant with zero,

Hence, the values of k for which the quadratic equation( k - 2) x² + ( 2k - 3) x + ( 5k - 6) = 0  has equal roots are k = 3, k =1.