Question

Q8. If both (x+1) and (x -1) are factors of ax² + x2 - 2x + b, find a and b.​

Answer 1

Step-by-step explanation:

a=1 b=-1

hope you understand

Answer 2

Correct Question :

Q8. If both (x+1) and (x -1) are factors of ax³ + x² - 2x + b, find a and b

Answer :

• a = 2
• b = -1

Step-by-step explanation :

  Let p(x) = ax³ + x² - 2x + b

• (x+1) is a factor

           x + 1 = 0

            x = -1

Since (x+1) is a factor of the given polynomial,

     when we substitute x = -1, we get p(-1) = 0

Put x = -1,

 a(-1)³ + (-1)² - 2(-1) + b = 0

 a(-1) + 1 + 2 + b = 0

   -a + 3 + b = 0

       b - a = -3

       b = a - 3

• (x-1) is a factor

          x - 1 = 0

            x = +1

Since (x - 1) is a factor of the given polynomial,

     when we substitute x = +1, we get p(1) = 0

Put x = +1,

a(1)³ + (1)² - 2(1) + b = 0

 a(1) + 1 - 2 + b = 0

   a - 1 + b = 0

     a + b = 1

     a + a - 3 = 1             [ b = a - 3 ]

     2a = 1 + 3

      2a = 4

      a = 4/2

       a = 2

=> b = a - 3

       = 2 - 3

       = -1

∴ a = 2 , b = -1