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

if a,b,c are in an AP and if the equations (b-c)x^2 + (c-a)x + (a-b)=0 and 2(c+a)x^2 + (b+c)x=0 HAVE A COMMON ROOT, then, prove that :- a^2, c^2, b^2 are in AP. [*x^2 refers to x square ]

if a,b,c are in an AP and if the equations (b-c)x^2 + (c-a)x + (a-b)=0 and 2(c+a)x^2 + (b+c)x=0 HAVE A COMMON ROOT, then, prove that :-


 a^2, c^2, b^2 are in AP.


[*x^2 refers to x square ]


 

Grade:

1 Answers

Ritika Kapoor
29 Points
10 years ago

hi shridhar,

well in eq.1, by observation we can say that x=1 is d root so a+b the odr root..

similarly in eq.2 x=0 is a root.. since common roots.. x=1 is also d soln of eq.2..

satisfting x=1 in eq.2 we get:

2a +3c +b =0

since a,b,c r in AP substituing a=b-d n c=b+d whre d is common difrence, we get

6b +d =0

hence a=7b =>a^2 =49b^2 similarly b^2 =25b^2

hence a^2 c^2 and b^2 r in AP wid common diff =24b^2

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free