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`        If the eqn x4 - 4x3 +a x2 +bx +1 = 0 has four positive roots, then show that a=6 and b=-4.`
8 years ago

Ramesh V
70 Points
```										since all roots are positive,
coeff. of x shld be negatuve i.e., b is negative
let roots be m(>0), n(>0), p(>0), q(>0)
m+n+p+q = 4
mn+np+pq+mp+mq+nq = a
mnp+mnq+npq+mpq = -b
mnpq = 1
For the objective case,
put m=n=p=q =1 (which satisfies eqns 1 and 4 above)
so a = 1+1+1+1+1+1 = 6
-b = 1+1+1+1 =4
so, a = 6 and b = -4
---
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Naga Ramesh
IIT Kgp - 2005 batch

```
8 years ago
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