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Shridhar Karpe Grade:
        

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 ]


 

6 years ago

Answers : (1)

Ritika Kapoor
29 Points
										

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

6 years ago
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