Question

$\text{Find the polynomial}p\left(x\right)=ax+b\text{such that}p\left(1\right)=2\&p\left(2\right)=5.$

• A. $3x-1$
• B. $-3x+5$
• C. $-2x+3$
• D. $2x+3$

Answer 1

The correct option is A $3x-1$

$\text{Given,}p\left(x\right)=ax+bp\left(1\right)=2,p\left(2\right)=5$

$p\left(1\right)=a+b=2a+b=2...\left(i\right)p\left(2\right)=2a+b=52a+b=5...\left(ii\right)$

$\text{Subtracting (i) from (ii), we get,}$
$2a+b=5\underset{–}{{}_{-}a\pm b{=}_{-}2}a=3$

$\therefore a=3$

$\text{Substituting in (i), we get,}$
$3+b=2b=2-3=-1$

$\text{Polynomial}p\left(x\right)=ax+b=3x-1$