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Question
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 - 5x - k = 0
Solution
The given quadric equation is 2x2 - 5x - k = 0, and roots are real
Then find the value of k.
Here, a = 2, b = -5 and c = k
As we know that D = b2 - 4ac
Putting the value of a = 2, b = -5 and c = k
= (-5)2 - 4 x (2) x (-k)
= 25 + 8k
The given equation will have real roots, if D ≥ 0
25 + 8k ≥ 0
8k ≥ -25
k ≥ -25/8
Therefore, the value of k ≥ -25/8.
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