Question

x-2
Polynomial P(x)=x²-ax+5 and
Q(x) = 2x³+5x-(a-3) when divided by
have
same remainders, then a is
equal to:​

Answer 1

${ \rm { \large \blue{Question \colon}}}$

${ \rm{ The \: equation}}$

${ \rm{p(x) = {x}^{2} - ax + 5}}$

${ \rm{q(x) = {2x}^{3} + 5x - (a - 3) }}$

${ \rm{divided \: by \: (x - 2)}}$

${ \rm{ \large \blue{Solution}}}$

${ \rm{Since \: x - 2 = 0 \implies x = 2}}$

${ \rm{First \: remainder }}$

${ \rm{p(x = 2) = {x}^{2} - ax + 5}}$

${ \rm{ \to {2}^{2} - 2x + 5 }}$

${ \rm{ \to 4 - 2 a + 5 }}$

${ \rm{ \to - 2a + 9 }}$

${ \rm{ \to 9 - 2a}}$

${ \rm{Second \: remainder}}$

${ \rm{q(x = 2) = {2x}^{3} + 5x - (a - 3) }}$

${ \rm{ \to {2 \times 2}^{3} + 5 \times 2 - (a - 3) }}$

${ \rm{ \to 16 + 10 - a + 3 }}$

${ \rm{ \to 29 - a }}$

${ \rm{the \: value \: of \: a = }}$

${ \rm {9 - 2a = 29 - a}}$

${ \rm{ \to 9 - 29 =2a - a }}$

${ \rm{ \to ( - 20 )= a }}$

${ \rm{ \to a = ( - 20)}}$

${ \rm{Ans \colon the \: common \: value \: of \: a = ( - 20)}}$