Exercise 4 | Wiskunde op Tilburg University

Solve

$7x^2-4x+2 > -3x^2+5x$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$\frac{2}{5}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\frac{4}{5}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$x< \frac{4}{5}$ or

$x>1$

Antwoord 4 correct

Fout

Antwoord 1 optie

$x< \frac{2}{5}$ or

$x>\frac{1}{2}$

Antwoord 1 feedback

Correct:

$7x^2-4x+2 > -3x^2+5x \Leftrightarrow 10x^2-9x+2 > 0$ .

Define

$f(x)=10x^2-9x+2$ . We determine the zeros of

$f(x)$ , hence we solve

$f(x)=0$ :

$D=9^2 - 4\cdot 10 \cdot 2 = 1$ .

Hence,

$x=\frac{2}{5}$ or

$x=\frac{1}{2}$ .

Via the sign chart (with for instance

$f(0)=2$ ,

$f(\frac{9}{20})=-0.025$ and

$f(1)=3)$ we find

$x< \frac{2}{5}$ or

$x>\frac{1}{2}$ .

Go on.

Antwoord 2 feedback

Wrong: Pay attention to the sign chart.

See Example 2 (film).

Antwoord 3 feedback

Wrong:

$x=\frac{-b\pm\sqrt{D}}{2a}$ .

See Extra explanation: zeros.

Antwoord 4 feedback

Wrong:

$x=\frac{-b\pm\sqrt{D}}{2a}$ .

See Extra explanation: zeros.