Question

$\text{If}(x+a)(x+b)=x^2+5x+6,\text{what is the value of}(a-b)\text{if}(a-b)>0?$

• A. 1

Answer 1

The correct option is A 1
$\text{We know that,}(x+a)(x+b)=x^2+\left(5\right)x+\left(6\right)$

$\text{By splitting the middle term,}{x}^2+\left(5\right)x+\left(6\right)\text{such that, the product}\text{is equal to 6 and sum or difference}\text{is equal to +5.}$


$\text{Hence,}{x}^2+5x+6=x^2+3x+2x+6$

$\text{Taking out the common factor,}\Rightarrow x(x+3)+2(x+3)\Rightarrow (x+3)(x+2)$

$\text{Comparing to}(x+a)(x+b)\text{and also}\text{given that}(a-b)>0.$

$\text{Hence}a=3\text{and}b=2$
$\therefore a-b=1$