Need help.. its urgent... !!
if a, b are roots of the equation px^2 + qx + r= 0, p is not equal to 0 and p,q,r are in A.P. and 1/a + 1/b = 4 , then find the value of |a-b|

Question

Need help.. its urgent... !!
if a, b are roots of the equation px^2 + qx + r= 0, p is not equal to 0 and p,q,r are in A.P. and 1/a + 1/b = 4 , then find the value of |a-b|

ganeshie8 · Answer

2q = p+r

ganeshie8 · Answer

1/a + 1/b = 4

(a+b)/(ab) = 4

-q/r =  4

ganeshie8 · Answer

then use :   (a-b)^2  =   (a+b)^2 - 4ab

ganeshie8 · Answer

once you have the numerical value, take the square root to get the value of |a-b|

anonymous · Answer

@ganeshie8  can you further explain it.. by the way thnxx... !!

ganeshie8 · Answer

(a-b)^2  =   (a+b)^2 - 4ab
               =  (4ab)^2 - 4ab

ganeshie8 · Answer

find the value of `ab` and plug it above^

ganeshie8 · Answer

ab =  r/p
  
2q = p+r
-q/r =  4
=> r/p = -1/9

ganeshie8 · Answer

So, ab =  -1/9

ganeshie8 · Answer

(a-b)^2  =   (a+b)^2 - 4ab
               =  (4ab)^2 - 4ab
               =  (4/9)^2 + 4/9

ganeshie8 · Answer

simplify and take the squareroot

ganeshie8 · Answer

you should get |a-b| =  2sqrt(13)/9