Question

Plz refer to the pic above


ignore That OR ;)

Answer 1

Let p(x) = x³ - 10x² + ax + b

p(x) would be a factor of (x-1) if p(1) = 0

so, p(1) = 0
       so, (1)³ - 10(1)² + a(1) + b =0
       so, 1-10 + a + b = 0
             so, a + b = 9 ...............................(1)

Similarly, p(2) = 0
      
         (2)³ -10(2)² + a(2) + b = 0
         8 - 40 +2a + b = 0
         so, 2a + b = 32 ...........................................(2)

BY subtracting Eqn (1) from (2)

 2a + b = 32
   a + b = 9
 
 a = 23 and b = -14