Question

24. If f(x) = x + x2- ax + b is divisible by x^2-x
is divisible by x2 - x write the values of a and b.​

Answer 1

Answer:

The value of a is 2 and b is 0

Step-by-step explanation:

$\text{If}\:f(x)=x^3+ x2- ax + b\text{is divisible by }x^2-x\text{ write the values of a and b}$

$\begin{array}{r|l}&x+2\\\cline{2-2}\\x^2-x&x^3+x^2-ax+b\\&x^3-x^2\\\cline{2-2}\\&\:\:\:\:\:2x^2-ax\\&\:\:\:\:\:2x^2-2x\\\cline{2-2}\\&\:\:\:\:\:(-a+2)x+b\\\cline{2-2}\end{array}$

$\text{since f(x) is divisible by}\:x^2-x\:\text{the remainder is 0}$

$\implies\:(-a+2)x+b=0$

$\implies\:-a+2=0\:and\:b=0$

$\implies\:a=2\:and\:b=0$