Question

12. If the polynomial x^3 + 2x^2 + ax + b has factors x+1 & X-1 find the
values of a&b​

Answer 1

Answer:

Step-by-step explanation:

the equation is x³+2x² +ax + b = 0

p(x)  = x³+2x²+ax+b = 0

the two zeros are -1 and 1

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

     = 3 + a +b = 0

     = a + b = -3 .............(1)

now

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

      = 1 - a + b = 0

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

now solve 1 and 2

a + b = -3

a - b = 1

------------

2a = -2

a = -1

now sub in (2)

-1 - b =1

b = -2

the value of a = -1 and b = -2