Question

Find the value of $a$ and $b$ if $x-1$ and $x-2$ are factors of $x^3-ax+b$

Answer 1

Consider given the expression,

$\Rightarrow x^3-ax+b$ and $x-1,x-2$ are the factor of this polynomial,

Given that, $x-1=0$ is the factor of $x^3-ax+b$

So, $x=1$ will be satisfied to $x^3-ax+b$

Hence,

$1^3-a.1+b=0$

$-a+b=-1$

$a-b=1$ ……(1)

Given that, $x-2=0$ is the factor of $x^3-ax+b$

So, x=2 will be satisfied to $x^3-ax+b$

$2^3-a.2+b=0$

$-2a+b=-2$

$2a-b=2$ ……(2)

Subtract equation 1^st from equation 2^nd,

$a=1$

put the value of a in equation 1^st,

$b=0$

Hence, this is the answer.