Algebra - GP

11

I have a tiny doubt:

If a,b,c are roots of x²-3x+p=0 and

Can a quadratic equation have three roots?

1

nope, i think he meant only a,b not a,b,c

1357

Manish Shankar ·2009-04-20 20:58:09

assuming a,b to be the roots of x²-3x+p=0
a+b=3 and ab=p
c+d=12 and cd=q
let r be the common ratio
b=ar, c=ar² and d=ar³

a+b=3 implies a(1+r)=3
and c+d=12 implies ar²)1+r)12

so we get r²=4

(q+p)/(q-p)=(cd+ab)/(cd-ab)=(r⁴+1)/(r⁴-1)=17/15

GP