# exo10 met tussenstap
n=$counter
!if $rounding=-1
    rounding=0
    !readproc $remarkdir/rounding.$taal
!endif
mathviewpanel=$module_title:x_1=:x_2=:x_3=:<=>:and
impossible=0
questiontype=0
checkfile=exos/checkfile2.proc
varlist=x
math=1
var1=5
# max number of arrows ->
cols=25
rows=6
kleuren=red,blue,green,orange,purple
kleuren=!shuffle $kleuren
color1=!item 1 of $kleuren
color2=!item 2 of $kleuren
exotext=$empty
question$n=!record 25 of lang/remarks.$taal
sometext=!record 6 of lang/remarks.$taal
helptext=!record 26 of lang/remarks.$taal
stext=!record 24 of lang/remarks.$taal
helptext=<a onmouseover="return escape('$helptext')">$stext</a>
raaklijn=!item 1 of $sometext
raken=!item 2 of $sometext
!if $usage=2
    image=0
!endif

!if $level=0
    R=$counter
!else
    R=$level
!endif        

!if $R=1
    keuze=!randitem 1,2
    #x(x+a)(x+b)=0
    a=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    b=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    !if $a=$b
	a=$[$a-1]
    !endif
    d=!randitem -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10
    !if $keuze=1
	c=$[$a*$b+$d]
        curve1=x^3+$[($a)+($b)]*x^2+($c)*x
        curve2=($d)*x
        C1=!htmlmath $curve1 = $curve2
        form1=!exec pari printtex($curve1) 
        formula$n= $form1 \,=\, $d x
    !else
        c=$[$a+$b+$d]
        curve1=x^3+($c)*x^2+$[($a)*($b)]*x
        curve2=($d)*x^2
        C1=!htmlmath $curve1 = $d*x^2
        form1=!exec pari printtex($curve1) 
        formula$n= $form1 \,=\, $d x^{2}
    !endif
    tussen=($curve1)-($curve2)
    x1=$[-1*$a]
    x2=$[-1*$b]
    x3=0
    tex_x1=$x1
    tex_x2=$x2
    tex_x3=$x3
    y1=0
    y2=0
    y3=0
    textanswer$n=!record 5 of lang/remarks.$taal
    #@ We ontbinden de vergelijking eerst in factoren, <br>dus de vergelijking wordt dan $C1 <br>
    texanswer$n=\left[ \begin{array}{l} x_1 = $tex_x1\\ x_2 = $tex_x2 \\ x_3 = $tex_x3  \end{array}\right.
    answer$n=$x1,$x2,$x3
    !if $image=1 or $teaching=1
	XRANGE=-15,15
	YRANGE=-50,50
	curve1=curve $color1,$curve1
	curve2=curve $color2,$curve2
	!readproc exos/image1.proc
    !endif
  !exit
!endif

!if $R=2
    keuze=!randitem 1,2
    #x(x+a)(x+b)=0
    a=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    b=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    !if $a=$b
	a=$[$a-1]
    !endif
    d=!randitem -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10
    e=!randitem -10,-9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9,10
    !if $keuze=1
        c=$[$a+$b+$d]
	f=$[$a*$b+$e]
	g=!randitem -5,-4,-3,-2,2,3,4,5,6
        curve1=x^3+($c)*x^2+($f)*x+($g)
        curve2=($d)*x^2+($e)*x+($g)
        C1=!htmlmath $curve1 = $curve2
        tot=!exec pari printtex($curve1)\
	printtex($curve2)
	
	form1=!line 1 of $tot 
	form2=!line 2 of $tot 
        formula$n= $form1 \,=\, $form2
    !else
        c=$[$a+$b+$d]
	f=$[$a*$b+$e]
        curve1=x^3+($c)*x^2+($f)*x
        curve2=($d)*x^2+($e)*x
        C1=!htmlmath $curve1 = $curve2
        tot=!exec pari printtex($curve1)\
	printtex($curve2)
	
	form1=!line 1 of $tot 
	form2=!line 2 of $tot 
        formula$n= $form1 \,=\, $form2
    !endif
    tussen=($curve1)-($curve2)
    x1=$[-1*$a]
    x2=$[-1*$b]
    x3=0
    tex_x1=$x1
    tex_x2=$x2
    tex_x3=$x3
    y1=0
    y2=0
    y3=0
    textanswer$n=!record 5 of lang/remarks.$taal
    #@ We ontbinden de vergelijking eerst in factoren, <br>dus de vergelijking wordt dan $C1 <br>
    texanswer$n=\left[ \begin{array}{l} x_{1} = $tex_x1\\ x_{2} = $tex_x2 \\ x_{3} = $tex_x3  \end{array}\right.
    answer$n=$x1,$x2,$x3
    !if $image=1 or $teaching=1
	XRANGE=-15,15
	YRANGE=-50,50
	curve1=curve $color1,$curve1
	curve2=curve $color2,$curve2
	!readproc exos/image1.proc
    !endif
  !exit
!endif

!if $R>2
    keuze=!randitem 1,2
    #x(x+a)(x+b)=0
    a=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    b=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,2,3,4,5,6,7,8,9
    !if $a=$b
	a=$[$a-1]
    !endif
    d=!randitem -1/4,-3/4,-1/3,-2/3,-1/2,1/2,1/3,2/3,1/4,3/4,1/5
    e=!randitem -1/4,-3/4,-1/3,-2/3,-1/2,1/2,1/3,2/3,1/4,3/4,1/5

    !if $keuze=1
        c=!exec pari ($a)+($b)+($d)
	f=!exec pari ($a*($b))+($e)
	g=!randitem -5,-4,-3,-2,2,3,4,5,6
        curve1=x^3+($c)*x^2+($f)*x+($g)
        curve2=($d)*x^2+($e)*x+($g)
        C1=!htmlmath $curve1 = $curve2
        tot=!exec pari printtex($curve1)\
	printtex($curve2)
	
	form1=!line 1 of $tot 
	form2=!line 2 of $tot 
        formula$n= $form1 \,=\, $form2
    !else
        c=!exec pari ($a)+($b)+($d)
	f=!exec pari ($a*($b))+($e)
        curve1=x^3+($c)*x^2+($f)*x
        curve2=($d)*x^2+($e)*x
        C1=!htmlmath $curve1 = $curve2
        tot=!exec pari printtex($curve1)\
	printtex($curve2)
	
	form1=!line 1 of $tot 
	form2=!line 2 of $tot 
        formula$n= $form1 \,=\, $form2
    !endif
    tussen=($curve1)-($curve2)
    x1=$[-1*$a]
    x2=$[-1*$b]
    x3=0
    tex_x1=$x1
    tex_x2=$x2
    tex_x3=$x3
    y1=0
    y2=0
    y3=0
    textanswer$n=!record 5 of lang/remarks.$taal
    #@ We ontbinden de vergelijking eerst in factoren, <br>dus de vergelijking wordt dan $C1 <br>
    texanswer$n=\left[ \begin{array}{l} x_{1} = $tex_x1\\ x_{2} = $tex_x2 \\ x_{3} = $tex_x3  \end{array}\right.
    answer$n=$x1,$x2,$x3
    !if $image=1 or $teaching=1
	XRANGE=-15,15
	YRANGE=-100,100
	curve1=curve $color1,$curve1
	curve2=curve $color2,$curve2
	!readproc exos/image1.proc
    !endif
  !exit
!endif
