Question

find the value of a and b so that the polynomial x3 -ax -13x +b when divided by x-1 and x+3 are factors​

Answer 1

Answer:

Let f(x)=x  

3

−ax  

2

−13x+b

Given that, (x−1) and (x+3) are factors of f(x)  

According to the factor theorem, if (x−a) is a factor of f(x), then f(a)=0.

Therefore, f(1)=0 and f(−3)=0

⇒f(1)=1−a−13+b=0

⇒b−a=12....(i)

And,

⇒f(−3)=−27−9a+39+b=0

⇒b−9a=12

∴ b=12+9a

Substituting the value of b in (i), we get:

12+9a−a=12

⇒8a=0

∴ a=0

b=12+9a

∴ b=12+9(0)=12

Hence, the value of a is 0 and that of b is 12.