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Q.

If exactly one root of the equation x2−(k−1)x+k(k+4)=0  lies between the roots of the equation x2−(k+3)x+k+2=0  then which of the following is/are CORRECT?

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a

k∈(−6,−2)

b

k∈[−6,−1)

c

k∈(3,6)

d

k∈[1,6)

answer is A, C.

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Detailed Solution

x2−(k+3)x+k+2=0⇒x=1,k+2   
Given exactly one root of f(x)=x2−(k−1)x+k(k+4)=0  lie between 1 and  k+2
⇒f(1)f(k+2)<0⇒(k+1)2(k+2)(k+6)<0⇒k∈(−6,−2)   

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