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Question
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 0
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Solution
The given quadric equation is 4x2 - 3kx + 1 = 0, and roots are real and equal
Then find the value of k.
Here, a = 4, b = -3k and c = 1
As we know that D = b2 - 4ac
Putting the value of a = 4, b = -3k and c = 1
= (-3k)2 - 4 x (4) x (1)
= 9k2 - 16
The given equation will have real and equal roots, if D = 0
Thus,
9k2 - 16 = 0
9k2 = 16
k2 = 16/9
`k=sqrt(16/9)`
`k=+-4/3`
Therefore, the value of `k=+-4/3` .
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