Question

If both $x+1$ and $x-1$ are factors of $a{x}^3+x^2+2a+b=0$, find the values of $a$ and $b$ respectively.

• A. $2,1$
• B. $2,2$
• C. $2,3$
• D. $2,4$

Answer 1

The correct option is A $2,1$

$a{x}^3+x^2+2a+b=0$
The factor of equation is x+1 ,x
Then put x=-1 or x=0in this equation
$a(-1{)}^3+(-1{)}^2+2a+b=0$
Or -a+1+2a+b=0
Or a+b=-1.............(1)
$a(0{)}^3+(0{)}^2+2a+b=0$
Or 2a+b=0.............(2)
Sub 1 &2
Then a=1 or a=1
Put value of a =1 in equ 1
Then b=2