Question

If both (x+1) and (x-1) are factor of ax^3+x^2-2x+b,find a and b

Answer 1

(x-1) and (x+1) are factors of the given polynomial.

x-1 = 0. ; x+1 = 0

x = 1. ; x = -1

Put x= -1,1 to find a and b

First,put x = 1

ax³+x²-2x+b = 0

a(1)³+(1)²-2(1)+b=0

a+1-2+b=0

a+b-1 = 0

a+b = 1 --------(1)

Put x = -1

a(-1)³+(-1)²-2(-1)+b = 0

a(-1)+1+2+b = 0

-a+b+3 = 0

-a+b = -3 -------(2)

(1)+(2)

a+b = 1
-a+b=-3
-----------
2b = -2

b = -2/2

b = -1

Put b= -1 in (1)

a+(-1) = 1

a-1 = 1

a=1+1

a=2

Therefore, a = 2 and b = -1

Hope it helps

★Snehitha2 (brainly benefactor)

Answer 2

Answer :-

If (x-1) and (x-2) are doctors of p(x), than p=(-1) and (1).

Now,

Putting p(-1)=ax^3+x^2-2x+b

=a(-1)^3+(-1)^2-2(-1)+b=0

=-a+1+2+b=0

=-a+b=-3 ...(1)

Putting p(1)=ax^3+x^2-2x+b

=a(1)^3+(1)^2-2(1)+b=0

=a+1-2+b=0

=a+b=1 ...(2)

Adding equation (1) and (2),

a+b-a+b=1-3

=2b=-2

=b=-1

Putting b=(-1) in equation (2),

a+(-1)=1

=a-1=1

=a=2

Therefore, a=2 and b= -1.