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Value(s) of k for which the quadratic eq...

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

A

`0`

B

`4`

C

`8`

D

`0,8`

Text Solution

Verified by Experts

The correct Answer is:
`D`
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.
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