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

Question

Sudheesh Singanamalla · Answer

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 · Answer

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

2 Answers