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 $=\frac{c}{a}$
$\Rightarrow \frac{c}{a}=-2$
$\Rightarrow \frac{(k-10)}{1}=-2$
$\Rightarrow k=8$
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