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: 12
        

IF a,b,c are real numbers and 3b^2-8ac<0,then the equation ax^4+bx^3+cx^2+5x+7=0 cannot have all roots real. prove this.

9 years ago

Answers : (1)

mycroft holmes
272 Points
							

The wording of the question is a dead giveaway.

 

Suppose all the roots r1, r2, r3 and r4 are real, then we must have

 

so that

 

Now, from Vieta's formulas, . So, if all roots are real, we must necessarily have  

 

or .

 

Since we are given that  it implies that all roots cannot be real.

9 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies

Get Extra Rs. 1,590 off

COUPON CODE: SELF10


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


Get Extra Rs. 233 off

COUPON CODE: SELF10

Ask Experts

Have any Question? Ask Experts

Post Question

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