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Question

If both sum of roots and product of roots of x2(λ25λ+5)x+(2λ23λ4)=0 are less than 1, then the range of λ is 
  1. (1,52)
  2. (1,4)
  3. [1,52]
  4. (1,52)


Solution

The correct option is D (1,52)
x2(λ25λ+5)x+(2λ23λ4)=0

Sum of roots <1
λ25λ+5<1λ25λ+4<0(λ1)(λ4)<0λ(1,4)     (1)

Product of roots <1
2λ23λ4<12λ23λ5<0(2λ5)(λ+1)<0λ(1,52)     (2)

From equations (1) and (2), we get
λ(1,52)

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