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If $x^{3}+x^{2}-a x+b$ is divisible by $\left(x^{2}-x\right)$, write the value of a and $b$.
If $x^{3}+x^{2}-a x+b$ is divisible by $\left(x^{2}-x\right)$, write the value of a and $b$.
CBSE | Class 10 | Excercise 2C | Maths | Polynomials | RS Aggarwal
If $x^{3}+x^{2}-a x+b$ is divisible by $\left(x^{2}-x\right)$, write the value of a and $b$.

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

x(x–1)=0
x(x-1)=0
⇒x=0 or x–1=0
\Rightarrow \mathrm{x}=0 \text { or } \mathrm{x}-1=0
⇒x=0 or x=1
\Rightarrow \mathrm{x}=0 \text { or } \mathrm{x}=1

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

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

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

$\Rightarrow \mathrm{b}=0$

And

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

$\Rightarrow \mathrm{a}=2$

i

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