Question

If the product of two of the roots $x^3-k{x}^2+5x+3=0$ is $-1$, then $k=$

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

Let $\alpha ,\beta ,\gamma$ are roots of $x^3-k{x}^2+5x+3=0$
Such that $\alpha \beta =-1$
Now $S_3=\alpha \beta \gamma =-3\Rightarrow \gamma =\frac{-3}{-1}=3$
Substituting $x=\gamma =3$ in equation, we get
${\left(3\right)}^3-k{\left(3\right)}^2+5\left(3\right)+3=0\Rightarrow 27-9k+15+3=0$

$\Rightarrow k=5$