Question

In copying a quadratic equation of the form $x^2+px+q=0$, the coefficient of $x$ was wrongly written as $-10$ in place in place of $-11$ and the roots were found to be $4$ and $6$. Then the difference between the roots of the correct equation is

Answer 1

The quadratic equation whose roots are $4,6$ is

$(x-4)(x-6)=0$

$\Rightarrow$ $x^2-6x-4x+24=0$

$\Rightarrow$ $x^2-10x+24=0$

It is mentioned that coefficient of $x$ is wrongly written as $-10$ instead of $-11$.

Thus, the new equation is

$x^2-11x+24=0$.
$\Rightarrow x^2-8x-3x+24=0$

$\Rightarrow x(x-8)-3(x-8)=0$
$\Rightarrow (x-8)(x-3)=0$
$\therefore x=8,3$

Hence, difference of roots $=8-3=5$.