Determine all $p$ such that the functions $f(x)=x^2+px+1$ and $g(x)=-3x^2+4x$ do not intersect.
Antwoord 1 correct
Correct
Antwoord 2 optie
For all $p$.
Antwoord 2 correct
Fout
Antwoord 3 optie
For no $p$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$p>0$
Antwoord 4 correct
Fout
Antwoord 1 optie
$0<p<8$
Antwoord 1 feedback
Correct: $x^2+px+1=-3x^2+4x \Leftrightarrow 4x^2+(p-4)x+1=0$.
No points of intersection means that $D<0$. $D=(p-4)^2-4\cdot 4\cdot 1=p^2-8p=p(p-8)$. Hence, $D=0$ for $p=0$ or $p=8$. A sign chart then gives $0<p<8$.
Go on.
No points of intersection means that $D<0$. $D=(p-4)^2-4\cdot 4\cdot 1=p^2-8p=p(p-8)$. Hence, $D=0$ for $p=0$ or $p=8$. A sign chart then gives $0<p<8$.
Go on.
Antwoord 2 feedback
Wrong: See Example 3 (film).
Antwoord 3 feedback
Wrong: See Example 3 (film).
Antwoord 4 feedback
Wrong: See Example 3 (film).