Find the values of k for each of the following quadratic equations, so that they have two equal roots.(i) `2x^2+k x+3=0` (ii) `k x(x-2)+6=0`

Explanation

(i) The given equation is
`2x^(2)+kx+3=0`
Comparing with `ax^(2)+kx+c=0`
a=2, b=k and c=3
`because` `because" ""Discriminant D"=b^(2)-4ac`
`impliesD=k^(2)-4xx2xx3`
`impliesD=k^(2)-24`
Since the equation has two equal roots
Therefore, D=0
Hence, `k^(2)-24=0`
`impliesk^(2)=24`
`impliesk=+-sqrt24=+-2sqrt6`
(ii) Given equation is `kx(x-2)+6=0`
`implieskx^(2)-2kx+6=0`
Comparing with `ax^(2)+bx+c=0`
a=k, b=-2k and c=6
`because"Discriminant D"=b^(2)-4ac`
`impliesD=(-2k)^(2)-4xxkxx6`
`impliesD=4k^(2)-24k`
For equal roots `D=0implies4k^(2)-24k=0`