If f(x)=x^3+px^2+qx+6,p,q,epsilon R, f'(x)<0 for largest possible interval [-5/3,-1], then p^2+q^2 = A)141 B)27 C)41 D)37

Ryland Solomon

Ryland Solomon

Answered question

2023-02-15

If f ( x ) = x 3 + p x 2 + q x + 6 , p , q , ϵ R , f ( x ) < 0 for largest possible interval [ 5 3 , 1 ], then p 2 + q 2 =
A)141
B)27
C)41
D)37

Answer & Explanation

usifaneledv2

usifaneledv2

Beginner2023-02-16Added 10 answers

The right answer is A 41

f ( x ) = 3 x 2 + 2 p x + q < 0 , x [ 5 3 , 1 ]
3 x 2 + 2 p x + q = ( x + 1 ) ( 3 x + 5 )
p = 4 , q = 5
p 2 + q 2 = 4 2 + 5 2 = 16 + 25 = 41
Answer: 41

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