Find the values `k` for which the quadratic equation `2x^2 + kx +3=0` has two real equal roots

Explanation

The given equation is `2x^(2)+kx+3=0.`
This is of the form `ax^(2)+bx+c=0,` where a=2, b=k and c=3.
`:." "D=(b^(2)-4ac)=(k^(2)-4xx2xx3)=(k^(2)-24).`
For real and equal roots, we much have
`D=0impliesk^(2)-24=0impliesk=+-sqrt(24)impliesk=+-sqrt(24)=+-2sqrt(6).`
Hence, `2sqrt(6)` and `-2sqrt(6)` are the required values of k.