Question 1170349

When {{{4x^2 -3x-8}}} is divided by {{{x-a}}}, the remainder is {{{2}}}. Find the value of {{{a}}}



......{{{4x-3+4a}}}
{{{x-a}}}|{{{4x^2 -3x-8}}}
......{{{4x^2-4ax}}}
.............{{{-3x+4ax}}}
.............{{{-3x+3a }}}
.................{{{4ax-3a}}}
.................{{{4ax-4a^2-8}}}
...................{{{-3a +4a^2-8}}}.................rearange
.................. ..{{{4a^2 -3a-8}}} -> reminder


given that the remainder is {{{2}}}

{{{4a^2 -3a-8=2}}}

{{{4a^2 -3a-8-2=0}}}

{{{4a^2 -3a-10=0}}}

{{{a=(-(-3)+-sqrt((-3)^2-4*4(-10)))/(2*4)}}}

{{{a=(3+-sqrt(9+160))/8}}}

{{{a=(3+-sqrt(169))/8}}}

{{{a=(3+-13)/8}}}

solutions:

{{{a=16/8}}}=>{{{a=2}}}
or
{{{a=-10/8}}}=>{{{a=-5/4}}}