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if a,b,c are inG.P find the ratio of ax2+bx+c=0

if a,b,c are inG.P find the ratio of ax2+bx+c=0


 

Grade:12

2 Answers

Sudheesh Singanamalla
114 Points
10 years ago

this question is not clear , what ratio do you want us to find

a:b:c

in a GP the numbers are always in the ratio of r : 1 with the previous number

so here the ratio is

1 : r : r2 where 'r' is the common term

 

Find 'r' and then we get the ratio.

 

Please approve !

Aniket Ghosh
5 Points
10 years ago

IF we are reqd to find the ratio between the roots of the equation ax2+bx+c=0.. then

Let the roots be Y and Z.So reqd to find is Z/Y.

Y+Z=-b/a

YZ=c/a

Let the common ratio of the gp be r

Y+Z=-r and YZ=r2

or (Y+Z)2=YZ

which gives Y2+Z2=-YZ

Dividing by YZ we get Y/z +Z/Y=-1

If Y/Z =m then we have m+1/m=-1

which is impossible as sum of a No and its reciprocal iS alwyz >2 or <-2..so the equation wont have any real roots

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