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```        if a,b,c are in g.p. , then the equation ax2 + bx + c = 0 & dx2+2ex+f=0 have a common root if d/a, e/b, f/c are in
(a) A.P.
(b)G.P.
(c)H.P.
(d)NONE OF THESE

```
8 years ago

SHAIK AASIF AHAMED
74 Points
```										Hello student,Please find the answer to your question belowa, b, c are in GP⇒b2=ac ------------(1)Now,ax2+2bx+c=0⇒x=−2b±sqrt(4b2−4ac)/2a⇒x=(−b±0)/a[Using(1)]⇒x=−b/aAlso,dx2+2ex+f=0⇒x=−2e±sqrt(4e2−4df)/2d⇒x=−e+sqrt(e2−df)/dNow, since the 2 equations have 1 common root, thus:-−b/a=−e+sqrt(e2−df)/d, ⇒d/a=(e/b)−sqrt(e2−df)/b,⇒d/a=e/b−sqrt((e2−df)/b2)⇒(e2−df)/b2=(e/b−d/a)2,⇒e2/b2−df/ac=(e/b−d/a)2,  [Using(1)]⇒(e/b)2−(d/a)(f/c)=(e/b)2−2(e/b)(d/a)+(d/a)2, ⇒−(da)(fc)=−2(e/b)(d/a)+(d/a)2,⇒f/c+d/a=2(e/b), ⇒d/a,e/b,f/careinAPHence a is the correct answer
```
3 years ago
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