Find the value of `k` for which the given equation has real and equal roots: `2x^2-10 x+k=0` `9x^2+3k x+4=0` `12 x^2+4k x+3=0` `2x^2+3x+k=0` `2x^2-k x+1=0` `k x^2-5x+k=0` `x^2+k(4x+k-1)+2=0` `x^2-2x(1+3k)+7(x+2k)=0` `(k+1)x^2-2(k-1)x+1=0`

Explanation

To find the value of \( k \) for which the given equations have real and equal roots, we need to ensure that the discriminant \( D \) of each quadratic equation equals zero. The discriminant \( D \) is given by the formula:

\[ D = b^2 - 4ac \]

where \( a \), \( b \), and \( c \) are the coefficients of the quadratic equation \( ax^2 + bx + c = 0 \).

...