Exercise 6 | Wiskunde op Tilburg University

Determine

$p$ such that

$f(x)=-3x^2+7$ and

$g(x)=4x-p$ have two points of intersection.

Antwoord 1 correct

Correct

Antwoord 2 optie

$p>-5\frac{2}{3}$

Antwoord 2 correct

Fout

Antwoord 3 optie

$p<-8\frac{1}{3}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$p<-5\frac{2}{3}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$p>-8\frac{1}{3}$

Antwoord 1 feedback

Correct:

$-3x^2+7=4x-p \Leftrightarrow -3x^2-4x+7+p=0$ .

Two points of intersection implies that

$D>0$ .

$D=(-4)^2-4\cdot-3\cdot(7+p)=100+12p$ . Hence,

$D>0$ if

$p>-8\frac{1}{3}$ .

Go on.

Antwoord 2 feedback

Wrong: Pay attention to the signs of the coefficients

$a$ ,

$b$ and

$c$ of the quadratic function of which you determine the zeros.

Try again.

Antwoord 3 feedback

Wrong: Note that for two points of intersection

$D>0$ is required of the equation that is put to zero.

See Extra explanation: zeros.

Antwoord 4 feedback

Wrong: Note that for two points of intersection

$D>0$ is required of the equation that is put to zero.

See Extra explanation: zeros.