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Question
Find the values of k for which the roots are real and equal in each of the following equation:
9x2 - 24x + k = 0
Solution
The given quadric equation is 9x2 - 24x + k = 0, and roots are real and equal
Then find the value of k.
Here, a = 9, b = -24 and c = k
As we know that D = b2 - 4ac
Putting the value of a = 9, b = -24 and c = k
= (-24)2 - 4 x (9) x (k)
= 576 - 36k
The given equation will have real and equal roots, if D = 0
Thus,
576 - 36k = 0
36k = 576
k = 576/36
k = 16
Therefore, the value of k = 16.
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