Question

help me out .20 number.

Answer 1

 ANS: Let p(x) = x3 - 10x2 +ax +b Using factor theorem we find that if p(x) is divided by x-1 the remainder, i.e. p(1) = 0

Therefore, p(1) = (1)3 - 10(1)2 + a(1) +b = 0

=> 1 - 10 +a +b =0

=> a+ b = 9
=> b = 9-a .........equation (1) 
In the same way if p(x) is divided by x-2 the remainder, i.e. p(2) = 0
Therefore, p(2) = (2)3 - 10(2)2 + a(2) +b = 0

=> 8 - 40 +2a +b =0
=> -32+2a+b=0...........equation (2)

Substituting the value of equation(1) in equation(2)
we get, -32 + 2a+9 -a = 0

=> a = 23

Substituting the value of a in equation (1)
we get b= 9- 23

=> b = -14
Hence, a=23 and b=-14
hope this helps..