1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Find the values of m such that exactly one root of the quadratic equation x2−(m−3)x+m=0 (m∈R) lies in the interval (1,2).

A
None of the above
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
(9,)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(10,)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
(,1)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is C (10,∞)Let, f(x)=x2−(m−3)x+m When exactly one root of f(x)=0 lies in the interval (1,2) Condition : (i) D>0 (ii) f(1).f(2)<0 Now, on solving it, (i) D>0 ⇒(m−3)2−4m>0 ⇒m2−6m+9−4m>0 ⇒m2−10m+9>0 ⇒(m−1)(m−9)>0 m∈(−∞,1)∪(9,∞) (ii) f(1).f(2)<0 ⇒(12−(m−3).1+m).(22−(m−3).2+m)<0 ⇒(1−m+3+m)(4−2m+6+m)<0 ⇒4(10−m)<0 ⇒m>10⇒m∈(10,∞) Now, taking both the above condition, we get m∈(10,∞)

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Location of Roots when Compared to two constants 'k1' & 'k2'
MATHEMATICS
Watch in App
Join BYJU'S Learning Program