Grade 12th passAlgebra

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

sohan goswami

8 Years agoGrade 12th pass

4 Answers

SR Roy

8 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

8 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

8 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

Approved Tutor Answer8 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.