Question

Find the value of k so that the equation $x^2-2x+(k+3)=0$ has one root equal to zero.

Answer 1

Consider the equation $x^2-2x+(k+3)=0$. Here, $a=1,b=-2,c=k+3$
Product of the roots $mn=\frac{c}{a}\therefore mn=\frac{k+3}{1}$
$\therefore mn=k+3$
Since '$m$' and '$n$' are the roots, and one root is zero then $m=n$ and $n=0$, $mn=k+3$
$\therefore m\left(0\right)=k+3\Rightarrow 0=k+3\therefore k=-3$