Solve $(x^2 -4)(x + 1) \geq -2(x + 2)$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$-2 \leq x \leq 1$
Antwoord 2 correct
Fout
Antwoord 3 optie
$x \geq -2$
Antwoord 3 correct
Fout
Antwoord 4 optie
$x\geq 1$
Antwoord 4 correct
Fout
Antwoord 1 optie
$-2\leq x \leq 0$ or $x\geq 1$
Antwoord 1 feedback
Correct:
$$\begin{align}
(x^2 - 4)(x + 1) = -2x - 4 & \Leftrightarrow x^3 + x^2 - 4x - 4 = -2x - 4\\
&\Leftrightarrow x^3 + x^2 - 2x = 0\\
& \Leftrightarrow x(x^2 + x - 2) = 0.
\end{align}$$
Hence, $x=0$ or $x^2+x-2=0$. This Quadratic function gives $x=1$ or $x=-2$. Via a sign chart (See Example 2 (film)) we get $-2\leq x \leq 0$ or $x\geq 1$.
Go on. $
Antwoord 2 feedback
Wrong: $x=0$ is also a solution of the corresponding equation.
Try again.
Antwoord 3 feedback
Wrong: $x=0$ is also a solution of the corresponding equation.
Try again.
Antwoord 4 feedback
Wrong: $x=0$ is also a solution of the corresponding equation.
Try again.