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multiple type correct:if a polynomial f(x)=4x^4-ax^3+bx^2-cx+5 (a,b,c belongs to R) has 4 positive real roots m,n,o,p such that m/2 + n/4 + o/5 + p/8 =1 then value of a is options:a- 20,b- 21, c- 19, d- 22

multiple type correct:if a polynomial f(x)=4x^4-ax^3+bx^2-cx+5  (a,b,c belongs to R) has 4 positive real roots m,n,o,p such that m/2 + n/4 + o/5 + p/8 =1 then value of a is options:a- 20,b- 21, c- 19, d- 22

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1 Answers

mycroft holmes
272 Points
6 years ago
Let M = m/2, N = n/4, O = o/5, and P = p/8
We see that mnop = 5/4 so that MNOP = 1/256
 
Also we have M+N+O+P = 1. From AM-GM inequality we have MNOP
 
Since MNOP = 256, we must have M = N = O = P = ¼.
 
so that m = ½, n = 1, o = 5/4 and p = 2.
 
Hence sum of roots = (m+n+o+p) = 19/4 = a/4. Hence a = 19
 
 

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