Solve $x^2+8x+1>-2x^2+2x-2$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$x=-1$
Antwoord 2 correct
Fout
Antwoord 3 optie
$x>-1$
Antwoord 3 correct
Fout
Antwoord 4 optie
$x<-1$
Antwoord 4 correct
Fout
Antwoord 1 optie
All $x$ except $x=-1$
Antwoord 1 feedback
Correct: $x^2+8x+1>-2x^2+2x-2 \Leftrightarrow 3x^2+6x+3 > 0$.
Define $f(x)=3x^2+6x+3$. We determine $f(x)=0$:
We use the quadratic equation. The discriminant is $D=0$, which implies that there is only one solution, $x=-1$.
Via the sign chart (for instance with $f(-2)=3$ and $f(0)=3$) we find that $f(x)$ is strictly positive for all $x$ expect for the zero $x=-1$.
Go on.
Define $f(x)=3x^2+6x+3$. We determine $f(x)=0$:
We use the quadratic equation. The discriminant is $D=0$, which implies that there is only one solution, $x=-1$.
Via the sign chart (for instance with $f(-2)=3$ and $f(0)=3$) we find that $f(x)$ is strictly positive for all $x$ expect for the zero $x=-1$.
Go on.
Antwoord 2 feedback
Wrong: $(-1)^2+8(-1)+1=-6 \ngtr -6=-2(-1)^2+2(-1)-2$.
Try again.
Try again.
Antwoord 3 feedback
Wrong: Pay attention to the sign chart.
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Try again.
Antwoord 4 feedback
Wrong: Pay attention to the sign chart.
Try again.
Try again.