Click to Chat

1800-2000-838

+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
Bhanu Kiran Grade: Upto college level
`        If the sum of the roots of the quadratic equation ax^2+ bx+c=0. is equal to the sum of the squares of their reciprocals, then a/c, b/a, c/b are in ....`
6 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear bhanu,
1 Given equation is ax2 + bx + c = 02 Let α, β be the roots. 3 α + β = -ba and αβ = ca  [Sum of the roots = -ba  and Product of the roots = ca.] 4 α + β = 1 α2+ 1 β2 [Given condition.]5 α + β= α2 + β2 α2 β2  [Simplify.]6 α + β = (α + β)² - 2αβα² β²   [Use α2 + β2 = (α + β)2 - 2α β.] 7 -ba =b²c² -2cac²a²  [Substitute the values.]8 -ba =b² - 2acc²  [Multiply and divide by a2 and simplify.]9 -ba =b²c²-2acc² [Simplify.]10 2acc²=b²c²+ba  [Simplify.]11 2a2c = ab2 + bc2 [Simplify.]12 2ab=bc+ca [Divide both sides by abc.]13 Therefore ab, bc, ca are in A.P

All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any                                query on askiitians forum and become an Elite        Expert        League            askiitian.

Sagar Singh
B.Tech, IIT Delhi

```
6 years ago
510 Points
```										let A,B  be the roots of this equation then,
A+B=-b/a  & AB=c/a          .................1
now it is given that sum of roots is equal to square of resiprocal of roots
so
A+B=1/A2 +1/B2
A+B=A2+B2 /(AB)2
A+B   = [(A+B)2 -2AB]/(AB)2
now putting value of A+B and AB from eq 1
-b/a =  [b2/a2 -2c/a] /c2/a2
ab2 +bc2 =2a2c                      ........................2
now let a/c,b/a,c/b are in HP then
a/b = [b/c + c/a]/2
ab2 + bc2 =2a2c
this result is similar to eq 2 so these terms are in HP.........

```
6 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details