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x2 - 9x + |k| = 0 has real roots. How many integer values can 'k' take?
1. 40
2. 21
3. 20
4. 41

Choice D. 41

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## Detailed Solution

Discriminant, D = 81 – 4|k|
If roots are real, D > 0
81 – 4|k| > 0
4|k| < 81
|k| < 20.25

Hence, –20.25 < k < 20.25
The integer values that k can take are –20, –19, –18 … 0 … 18, 19 and 20.

41 different values (Remember to include 0. Answer choice 'A' will definitely be 40

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