badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 11

                        

For what value of `a`, does the equation ax²-(a+1)x+3=0, have roots lying between 1 and 2?

3 years ago

Answers : (4)

Arun
24738 Points
							
The interval doesn’t include the boundary points 1,2. So the roots can’t be 1 or 2.
So the sum will be greater than 2 and less than 4. Similarly the product will be more than 1 and less than 4.
sum=a+1/a=1+1/a and product=3/a
2
=>1
Here the a is always positive as the sum and product of roots is positive. so we can safely multiply a on both sides in the above inequalities.
=>a
=> a belongs to the interval (1/3,1) AND a belongs to (3/4,3)
Both the conditions have to be true at the same time.
hence, a belongs to the interval (3/4,1)
3 years ago
Rahul Jain
10 Points
							Just a bit of a modification there...For roots to be real D≥0a²+1+2a-12a≥0a²-10a+1≥0Therefore, a  5+2√6Also 3/4 
						
3 years ago
Abu Azbar
27 Points
							No real values of a make the roots of the equation ax^2-(a+1)x+3 between 1.   and   3..So the approved answer is wrong
						
2 years ago
yathartha gupta
71 Points
							Home » Forum » Algebra » For what value of `a`, does the equation...For what value of `a`, does the equation ax²-(a+1)x+3=0, have roots lying between 1 and 2?one month agoAnswers : (3)The interval doesn’t include the boundary points 1,2. So the roots can’t be 1 or 2.So the sum will be greater than 2 and less than 4. Similarly the product will be more than 1 and less than 4.sum=a+1/a=1+1/a and product=3/a2=>1Here the a is always positive as the sum and product of roots is positive. so we can safely multiply a on both sides in the above inequalities.=>a=> a belongs to the interval (1/3,1) AND a belongs to (3/4,3)Both the conditions have to be true at the same time.hence, a belongs to the interval (3/4,1) Ok
						
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details