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

# Find the value of m such that roots of the quadratic equation x2−(m−3)x+m=0 (m∈R) are positive

A
[9,)
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
[1,9]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
(3,9)
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
(,9]
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

## The correct option is A [9,∞)Condition: When roots are positive : (i) D≥0 (ii) Sum of roots >0 (iii) product of roots >0 Now, solve it one by one (i) D≥0 ⇒(m−3)2−4m≥0 ⇒m2−6m+9−4m≥0 ⇒m2−10m+9>≥ ⇒(m−1)(m−9)≥0 m∈(−∞,1]∪[9,∞) (ii) Sum of roots >0 ⇒ Sum of roots =(m−3)>0 ⇒(m−3)>0⇒m>3 m∈(3,∞) (iii) Product of roots >0 ⇒ Product of roots =m1>0 m>0⇒m∈(0,∞) Now, taking intersection of all the three conditions, we get m∈[9,∞)

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Introduction to Quadratic Equations and Polynomials
MATHEMATICS
Watch in App
Join BYJU'S Learning Program