Value(s) of `k` for which the quadratic equation `2x^(2)-kx+k=0` has equal roots is/are

Options

A. `0`
B. `4`
C. `8`
D. `0,8`

Answer

D

Explanation

Given equation is `2x^(2)-kx+k=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=2,b=-k` and `c=k`
For equal roots, the discriminant must be zero.
i.e., `D=b^(2)-4ac=0`
`= (-k)^(2)-4(2)k=0`
`implies k^(2)-8k=0`
`implies k(k-8)=0`
`:. k=0,8`
Hence the required values of `k` are 0 and 8.