If f(x)=x^3+Ax^2+Bx-3 and if f(1)=4 andf(-1)=-6, what is the value of 2A+B? (A) 12 (B) 8 (C) 0 (D) -2

Elianna Lawrence 2022-07-26 Answered
If f ( x ) = x 3 + A x 2 + B x 3 and if f(1)=4 and f(-1)=-6, what is the value of 2A+B?
(A) 12
(B) 8
(C) 0
(D) -2
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Answers (2)

Marisa Colon
Answered 2022-07-27 Author has 18 answers
f ( x ) = x 3 + A x 2 + B x 3 and if f(1)=4 and f(-1)=-6, what is the value of 2A+B?
f ( 1 ) = 4 = 1 + A + B 3 A + B = 6.....(I)
f ( 1 ) = 6 = 1 + A B 3 A B = 2......(II)
2A =4
A = 2 A + B = 6 B = 4
Hence 2A+B= 4+4=8
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Shannon Andrews
Answered 2022-07-28 Author has 5 answers
We have that f(1)=4 and that f(-1)=6. This gives us:
f ( 1 ) = 4 ( 1 ) 3 + A ( 1 2 ) + B ( 1 ) 3 = A + B 2
f ( 1 ) = 6 = ( 1 ) 3 + A ( 1 2 ) + B ( 1 ) 3 = A B 4
So, we have:
4=A+B-2....(1)
-6=A-B-4.....(2)
Adding (1) and (2) gives us:
4+(-6)=(A+B-2)+(A-B-4)
-2=2A-6=> 2A=4
Now, we subtract both of them and get:
4-(-6)=(A+B-2)-(A-B-4)
10=2B+2 => B=4
Therefore, 2A+B = 4+4 = 8 , which is option (B)
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