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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.
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 --- Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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
---
Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly.We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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