Question

If both x+1 and x-1 are factors of ax^3 +x^2-2x+b,find the values of a and b

Answer 1

★ CUBIC RESOLUTION ★

Given function :

ax^3 + x² - 2x + b = 0

For given that x - 1 and x + 1 are factors respectively ,

HENCE , x = 1 and -1 will satisfy the cubic equation

x = 1

a + 1 - 2 + b = 0

x = -1

-a + 1 + 2 + b = 0

Two respective linear equivalents are obtained

a + b = 1

-a + b = -3

Solving them will yield

a = 2 and b = -1

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Answer 2

Given cubic polynomial is  = ax³+x²-2x+b 
also  x+1 and x-1 are factors of this polynomial , thus 
x= -1,1 must satisfy this equation 

Now put x = -1 in the given polynomial we get 
a(-1)³+(-1)²-2(-1)+b = 0 
=> -a+b+2 +1 = 0 
=> b-a = 3 ------------------1
Now put x = 1 , we get 
a(1)³+(1)²-2(1)+b=0
=>  a+b=1 ----------------2
solving these two 
 a = 2 and b = -1