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Question

Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) 2x2+kx+3=0
(ii) kx(x2)+6=0

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Solution

i)
If 2x2+kx+3=0 has equal roots, then b24ac=0.
Here, a=2,b=k,c=3

x2+kx+3=0b24ac=0k24(2)(3)=0k2=24k=±24=±26

ii)
If kx22kx+6=0 has equal roots, then b24ac=0.
Here, a=k,b=2k,c=6

kx(x2)+6=0kx22kx+6=04k24(k)(6)=04k224k=04k(k6)=0
For k=0, equation is not quadratic.
k=6

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