Question

If x – 1 and x + 1 are factors of ax3 + x2 -2x + b, then find the values of ‘a’ and ‘b’

Answer 1

Answer:

Given,x-1 and x+1 are factors of p(x),

p(x) = ax³+x²-2x+b

So, x-1=0

x= 1

p(1)=a(1)³+(1)²-2(1)+b=0

a+1-2+b=0

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

And, x+1=0

x= -1

p(-1) = a(-1)³+(-1)²-2(-1)+b = 0

-a+1+2+b=0

3-a+b=0

Equate (1) & (2),

a+b-1 = 3-a+b

a+b+a-b = 3+1

2a = 4

a = 2 ----------(3)

Substitute eq(3) in eq(1),

2+b-1=0

b+1=0

b= -1

Hence, a = 2 & b = -1

Answer 2

Answer:

Question :-

.

Given :

Let's take (x+1) & (x-1) as the factors .

Required to find :-

Values of a and b ?

Solution :

Given expression :-

As ,

(x+1) & (x-1) are the factors

Let ,

x + 1 = 0

x = -1

Now substitute this value in place of x in the above expression

Similarly,

(x - 1) is a factor

So Let ,

x - 1 = 0

x = 1

Substitute this value in place of x in p(x)

Here , +2 & -2 will get cancelled due to their opposite signs

Now,

Consider equation - 1

Here substitute the value of a in it

Step-by-step explanation: