Exercise 2 | Wiskunde op Tilburg University

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.