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The value of k for which the number 3 lies between the roots of equation x^2 + (1 - 2k)x + (k^2 - k - 2) = 0 is given by A) 2 B) k > 2 C) 2 D) k > 5 [Full Explaination needed]

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one year ago

2056 Points
```							note that the graph of y= f(x)= x^2 + (1 - 2k)x + (k^2 - k - 2) would be an upward parabola. so, a necessary and sufficient condition for 3 to lie in between roots is f(3) should be less than 0. this is in effect the same as applying intermediate value theorem as  f is continuous.here, f(3)= 9 + 3(1 –  2k) + k^2 - k - 2 must be less than 0.or k^2 – 7k + 10 must be less than 0.or (k – 2)(k – 5) must be less than 0.so that Ans: k should lie in (2, 5).your option A and C are wrongly typed so idk what they are.but D is definitely wrong and B is partially correct.anways, the ques has been answered.kindly approve :)
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one year ago
23 Points
```							Sir, I think there was a problem in placing the optionsThe Updated Options areA) 2$<$k$<$5B) k > 2C) 2$<$k$<$3D) k > 5
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one year ago
2056 Points
```							yeah so obviously option A is correct as it is the same as (2, 5).if any other doubt, feel free to ask. kindly approve :)
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one year ago
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