Question

If the roots $x_1$ and $x_2$ of the equation $x^2+px+12=0$ possess the property $x_1-x_2=1$, then the value of $p$ can be

• A. $p=7$
• B. $p=14$
• C. $p=-7$
• D. $p=-14$

Answer 1

Answer: (A), (C)

$p=7$
$p=-7$

If $x_1,x_2$ are the roots of $x^2+px+12=0$, then

$x_1+x_2=-p,x_1{x}_2=12$
Also given $x_1-x_2=1$, squaring both sides, $x_1^2+x_2^2-2x_1{x}_2=1$
$\Rightarrow (x_1+x_2{)}^2-4x_1{x}_2=1$

$\Rightarrow p^2-48-1=0$
$\Rightarrow p^2=49$

$\Rightarrow p=-7,7$