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If a,b,c are in AP such that a+b+c=0,then roots of the equation px 2 +qx+b=0;(pq≠0) are a.real and identical b.real and distinct c.imaginary d.none of these

If a,b,c are in AP such that a+b+c=0,then roots of the equation px2+qx+b=0;(pq≠0) are


a.real and identical


b.real and distinct


c.imaginary


d.none of these

Grade:12th Pass

2 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Menka,

 

Now a,b,c are in AP. So 2b=a+c

a+b+c = 0, will give 3b=0 or b=0.

 

Hence the QE becomes, px^2 + qx = 0.

 

Hence one root is 0, and the other is -q/p.

Since pq is not zero, the value -q/p can never be 0.

Hence real and distinct roots. Option (B).

 

Hope it helps.

 

Best Regards,

Ashwin (IIT Madras).

ankitesh gupta
63 Points
8 years ago

 

 

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