If x3 + x2 − ax + b is divisible by
Question:

If $x^{3}+x^{2}-a x+b$ is divisible by $\left(x^{2}-x\right)$, write the values of $a$ and $b$.

 

Solution:

Equating $x^{2}-x$ to 0 to find the zeros, we will get

$x(x-1)=0$

$\Rightarrow x=0$ or $x-1=0$

$\Rightarrow x=0$ or $x=1$

Since, $x^{3}+x^{2}-a x+b$ is divisible by $x^{2}-x$

Hence, the zeros of $x^{2}-x$ will satisfy $x^{3}+x^{2}-a x+b$

$\therefore(0)^{3}+0^{2}-a(0)+b=0$

$\Rightarrow b=0$

and

$(1)^{3}+1^{2}-a(1)+0=0 \quad[\because b=0]$

$\Rightarrow a=2$

 

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