Question

12. If x + 2x² + ax + b has factors x+1 and x-1, then find a and b.
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Answer 1

Answer:

a= -1

b= -2

Step-by-step explanation:

If x+1 and x-1 are the factors of x+2x^2+ax+b, then the equation have two values of x, x= -1 and x= 1.

substituting the values of x in the equation, we get,

• 1 + 2×1 + a + b (putting the value of x= 1)

= a+b+3 (eq.1)

• -1 + 2×1 + (-1)a + b(putting the value of x=-1)

= -1 + 2 - a + b

= b-a+1 (eq.2)

From (eq.2)

b-a+1=0

b+1=a

substituting this value of a in (eq.1)

a+b+3=0

b+1+b+3=0

2b+4=0

b= -4/2

b= -2

And a= b+1

a= -2+1

a= -1