Question

Using remainder theorem find the value of a If the division of x3+5x2-ax+6 by ( x-1 ) leaves a remainder 2a

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{When\;x^3+5x^2-a\,x+6\;is\;divided\;by\;(x-1),}$

$\textsf{leaves remainder 2a}$

$\underline{\textbf{To find:}}$

$\textsf{The value of 'a'}$

$\underline{\textbf{Solution:}}$

$\mathsf{P(x)=x^3+5x^2-a\,x+6}$

$\textsf{The remainder when P(x) is divided by (x-1) is 2a}$

$\textsf{Using Remainder theorem,}$

$\mathsf{P(1)=2a}$

$\mathsf{1^3+5(1)^2-a(1)+6=2a}$

$\mathsf{1+5-a+6=2a}$

$\mathsf{1+5+6=2a+a}$

$\mathsf{3a=12}$

$\implies\boxed{\mathsf{a=4}}$

$\underline{\textbf{Remainder theorem:}}$

$\boxed{\begin{minipage}{7cm} \\\textsf{The remainder when P(x) is divided by (x-a)}\\\\\textsf{is P(a)}\\ \end{minipage}}$

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