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plz sir help me out in this question, i will be very thankfull. plz explain me this The number of values of k for which the equation x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1) are (A) Three (B) Two (C) Infinitely many (D) No values of k satisfies the requirement

plz sir help me out in this question, i will be very thankfull. plz explain me this
The number of values of k for which the equation x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1) are
(A) Three (B) Two
(C) Infinitely many (D) No values of k satisfies the requirement     

Grade:12th pass

4 Answers

SR Roy
128 Points
6 years ago
The number of values of k for which the equation x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1) are(A) Three (B) Two(C) Infinitely many (D) No values of k satisfies the requirement     
Option C infinitely many
Hope this will help you
Samyak Jain
333 Points
5 years ago
 x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1)
It is easy to solve this question using location of roots.
So we have f(x) = x2 – 3x + k 
i) f(0) > 0  i.e. k > 0            …..........(1)
ii) f(1) > 0  i.e. 1 – 3 + k > 0  i.e. k > 2  …........(2)
iii) D > 0  i.e. 9 – 4k > 0  i.e. k
Taking in intersection of (1),(2),(3), we get 2
So there are infinitely many values of k for given condition.
Samyak Jain
333 Points
5 years ago
x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1)
It is easy to solve this question using location of roots.
So we have f(x) = x2 – 3x + k 
i) f(0) > 0  i.e. k > 0            …..........(1)
ii) f(1) > 0  i.e. 1 – 3 + k > 0  i.e. k > 2  …........(2)
iii) D > 0  i.e. 9 – 4k > 0  i.e. k
Taking in intersection of (1),(2),(3), we get 2
So there are infinitely many values of k for given condition.
SR Roy
128 Points
5 years ago
x2 – 3x + k = 0 has two distinct roots lying in the interval (0, 1)It is easy to solve this question using location of roots.So we have f(x) = x2 – 3x + k i) f(0) > 0 i.e. k > 0 …..........(1)ii) f(1) > 0 i.e. 1 – 3 + k > 0 i.e. k > 2 …........(2)iii) D > 0 i.e. 9 – 4k > 0 i.e. kTaking in intersection of (1),(2),(3), we get 2So there are infinitely many values of k for given condition.

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