10 The roots of the equation \( 2 x^{2}-4 x+k=0 \) are real and equal if \( k \) is equal to 1) -2 2) 2 3) -4 4) 4

For the roots of the quadratic equation \( 2x^2 - 4x + k = 0 \) to be real and equal, the discriminant must be zero. The discriminant \( D \) is given by \( D = b^2 - 4ac \). Here, \( a = 2 \), \( b = -4 \), and \( c = k \). So we have: \[ D = (-4)^2 - 4(2)(k) = 16 - 8k \] Setting the discriminant to zero for equal roots: \[ 16 - 8k = 0 \implies 8k = 16 \implies k = 2 \] Thus, the correct answer is \( k = 2 \).