Question

(x-2) and (x-3) are factors of x³+ax²+bx-30 , find a and b.

Answer 1

Answer:

a= -10 and b= 31

Step-by-step explanation:

let f(x) = x³+ax²+bx-30

since (x-2) and (x-3) are the factors

      therefore f(2)=0 and f(3)=0  by remainder and factor theorem

since f(2)=0

         (2)³+a(2)²+b(2)-30 =0

         8+4a+2b-30 =0

         4a+2b-22=0

          2a+b=11 ----------eq 1

since f(3)=0

         (3)³+a(3)²+b(3)-30 =0

          27+9a+3b -30 =0

          9a+3b-3=0

           3a+b=1 ------------eq 2

 subtract  eq 1 from  eq 2

when we solve these linear equations in two variables we will get the value

   a= -10  and b= 31