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Question
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
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Solution
The given quadric equation is `kx^2-2sqrt5x+4=0`, and roots are real and equal
Then find the value of k.
Here, a = k, `b=-2sqrt5`, and c = 4
As we know that D = b2 - 4ac
Putting the value of a = k, `b=-2sqrt5`, and c = 4
`=(-2sqrt5)^2-4xxkxx4`
= 20 - 16k
The given equation will have real and equal roots, if D = 0
Thus,
20 - 16k = 0
16k = 20
k = 20/16
k = 5/4
Therefore, the value of k = 5/4.
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