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Question
Find the values of k for which the roots are real and equal in each of the following equation:
2kx2 - 40x + 25 = 0
Solution
The given quadric equation is 2kx2 - 40x + 25 = 0, and roots are real and equal
Then find the value of k.
Here, a = 2k, b = -40 and c = 25
As we know that D = b2 - 4ac
Putting the value of a = 2k, b = -40 and c = 25
= (-40)2 - 4 x (2k) x (25)
=1600 - 200k
The given equation will have real and equal roots, if D = 0
Thus,
1600 - 200k = 0
200k = 1600
k = 1600/200
k = 8
Therefore, the value of k = 8.
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