# Onvolledige VKV (c=0)

#### Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. $$-3(3x^2-3x)=-(10x^2-9x)$$
2. $$3(8x^2-3x)=-(-31x^2+9x)$$
3. $$-5(6x^2-9x)=-(22x^2-70x)$$
4. $$12x^2+15x=8x^2+3x$$
5. $$3x^2-22x=0$$
6. $$-6x^2+18x=0$$
7. $$-2(4x^2-9x)=-(10x^2+2x)$$
8. $$-3(4x^2+10x)=-(11x^2+31x)$$
9. $$8x^2-23x=7x^2+2x$$
10. $$-4(9x^2-5x)=-(41x^2-22x)$$
11. $$3x^2-21x=0$$
12. $$8x^2+0x=0$$

#### Los de vierkantsvergelijking op zonder de discriminant te gebruiken

##### Verbetersleutel

1. $$-3(3x^2-3x)=-(10x^2-9x) \\ \Leftrightarrow -9x^2+9x=-10x^2+9x \\ \Leftrightarrow -9x^2+9x+10x^2-9x= 0 \\ \Leftrightarrow x^2+0x=0 \\ \Leftrightarrow x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------$$
2. $$3(8x^2-3x)=-(-31x^2+9x) \\ \Leftrightarrow 24x^2-9x=31x^2-9x \\ \Leftrightarrow 24x^2-9x-31x^2+9x= 0 \\ \Leftrightarrow -7x^2+0x=0 \\ \Leftrightarrow -7x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-7} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------$$
3. $$-5(6x^2-9x)=-(22x^2-70x) \\ \Leftrightarrow -30x^2+45x=-22x^2+70x \\ \Leftrightarrow -30x^2+45x+22x^2-70x= 0 \\ \Leftrightarrow -8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------$$
4. $$12x^2+15x=8x^2+3x \\ \Leftrightarrow 4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------$$
5. $$3x^2-22x=0 \\ \Leftrightarrow x(3x-22) = 0 \\ \Leftrightarrow x = 0 \vee 3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------$$
6. $$-6x^2+18x=0 \\ \Leftrightarrow x(-6x+18) = 0 \\ \Leftrightarrow x = 0 \vee -6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-6} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------$$
7. $$-2(4x^2-9x)=-(10x^2+2x) \\ \Leftrightarrow -8x^2+18x=-10x^2-2x \\ \Leftrightarrow -8x^2+18x+10x^2+2x= 0 \\ \Leftrightarrow 2x^2-20x=0 \\ \Leftrightarrow x(2x-20) = 0 \\ \Leftrightarrow x = 0 \vee 2x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{2} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------$$
8. $$-3(4x^2+10x)=-(11x^2+31x) \\ \Leftrightarrow -12x^2-30x=-11x^2-31x \\ \Leftrightarrow -12x^2-30x+11x^2+31x= 0 \\ \Leftrightarrow -x^2-1x=0 \\ \Leftrightarrow x(-x-1) = 0 \\ \Leftrightarrow x = 0 \vee -x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-1} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------$$
9. $$8x^2-23x=7x^2+2x \\ \Leftrightarrow x^2-25x=0 \\ \Leftrightarrow x(x-25) = 0 \\ \Leftrightarrow x = 0 \vee x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{1} = 25 \\ V = \Big\{ 25; 0 \Big\} \\ -----------------$$
10. $$-4(9x^2-5x)=-(41x^2-22x) \\ \Leftrightarrow -36x^2+20x=-41x^2+22x \\ \Leftrightarrow -36x^2+20x+41x^2-22x= 0 \\ \Leftrightarrow 5x^2+2x=0 \\ \Leftrightarrow x(5x+2) = 0 \\ \Leftrightarrow x = 0 \vee 5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------$$
11. $$3x^2-21x=0 \\ \Leftrightarrow x(3x-21) = 0 \\ \Leftrightarrow x = 0 \vee 3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{3} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------$$
12. $$8x^2+0x=0 \\ \Leftrightarrow 8x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{8} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------$$
Oefeningengenerator vanhoeckes.be/wiskunde 2024-08-09 04:00:30