Question

If X-1 and x+2 are the factors of x3+10x2+ax+b then find the values of a and b

Answer 1

Answer:

p(x) = x^3+10x^2+ax+b .................i

x-1 = 0

x = 1 ...........ii

x+2 = 0

x = -2 ...........iii

By substituting ii in i,

p(1) = 1^3+10(1)^2+a(1)+b

     = 1+100+a+b

   0= 101+a+b............iv

By substituting iii in i,

p(-2) = (-2)^3+10(-2)^2+a(-2)+b

        = -8+400-2a+b

    0 = 392-2a+b..........v

In iv,

a+b = -101

In v,

2a-b = 392

By solving these eqns,

You will get:

a= 97

b= -198