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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 + kx + 9 = 0
Solution
The given quadric equation is 4x2 + kx + 9 = 0, and roots are real and equal
Then find the value of k.
Here, a = 4, b = k and c = 9
As we know that D = b2 - 4ac
Putting the value of a = 4, b = k and c = 9
= (k)2 - 4 x (4) x (9)
= k2 - 144
The given equation will have real and equal roots, if D = 0
Thus,
k2 - 144 = 0
k2 = 144
`k=sqrt144`
k = ± 12
Therefore, the value of k = ± 12.
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