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Question

If f(x)=x3+px2+qx+6, p,q,ϵR, f(x)<0 for largest possible interval [53,1], then p2+q2=



Your Answer
A

141

Your Answer
B

27

Correct Answer
C

41

Your Answer
D

37


Solution

The correct option is A

41


f(x)=3x2+2px+q<0, x[53,1]

3x2+2px+q=(x+1)(3x+5)

p=4, q=5

p2+q2=42+52=16+25=41

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