CAT 2023 Slot 1 Solved Paper

Given that -2 is a root of the given cubic equation.
⇒ Dividing the given equation by $\left(\mathit{x}+2\right)$, Using the Horners method of synthetic division:
coefficient of ${\mathit{x}}^2$ is 1 , and coefficient of $\mathit{x}$ is $\left(2\mathit{r}+1\right)-2=2\mathit{r}-1$ and the constant term $=\left(4\mathit{r}-1\right)-2\left(2\mathit{r}-1\right)=1$.
⇒ The quadratic obtained by dividing the cubic $={\mathit{x}}^2+\left(2\mathit{r}-1\right)\mathit{x}+1=0$, Since, this equation has 2 real
roots ⇒ Discriminant should be greater than 0
$\Rightarrow {\left(2\mathit{r}-1\right)}^2>4\Rightarrow 2\mathrm{r}-1>2$ or or .
⇒ Minimum possible non-negative integer value of $\mathit{r}$ is 2 .