 ×     #### Thank you for registering.

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

Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

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
```
If a ,b,c are positive real numbers such that the equations a(x^2) + bx + c =0 and b(x^2) + cx + a = 0 , have a common root, then 1)a + bw + c(w^2) = 0 2)a + b(w^2)+ cw = 0 3)a^3 + b^3 + c^3 = 3abc 4)all of the above

```
2 years ago

```							let the common root be w.then a(w^2) + bw + c =0 and b(w^2) + cw + a =  0 subtracting,(a-b)(w^2) +(b-c)w + c-a =  0 so w=1 or (c-a)/(a-b)if w=1, then a+b+c=0, but a, b and c are positive so this cant be true.if w=(c-a)/(a-b), then on putting this value in the original equation, and simplifying we geta^2+b^2+c^2-ab-bc-ca=0or [a + bw + c(w^2)][a + b(w^2)+ cw ]=0so, either  a + b(w^2)+ cw =0, or a + bw + c(w^2)=0.and a^3 + b^3 + c^3 –3abc= (a+b+c)(a + b(w^2)+ cw)( a + bw + c(w^2))=0note that if a + bw + c(w^2) =0, that automatically implies )a + b(w^2)+ cw =0 [taking conjugate]so, so, option (4) is correct.
```
2 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »  ### 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