If the product of the roots of the equation
Question:

If the product of the roots of the equation $x^{2}-3 x+k=10$ is $-2$, then the value of $k$ is

(a) −2
(b) −8
(c)  8
(d) 12

Solution:

(c)  8

It is given that the product of the roots of the equation $x^{2}-3 x+k=10$ is $-2$.

The equation can be rewritten as :

$x^{2}-3 x+(k-10)=0$

Product of the roots of a quadratic equation $=\frac{c}{a}$

$\Rightarrow \frac{c}{a}=-2$

$\Rightarrow \frac{(k-10)}{1}=-2$

$\Rightarrow k=8$