# Onvolledige VKV (c=0)

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

1. $$-4x^2-20x=0$$
2. $$8x^2-19x=0$$
3. $$3x^2-7x=0$$
4. $$-5(-6x^2+3x)=-(-33x^2+25x)$$
5. $$-8x^2-14x=-7x^2-10x$$
6. $$-5(8x^2+3x)=-(42x^2+15x)$$
7. $$4(-6x^2-5x)=-(26x^2+31x)$$
8. $$4x^2+11x=0$$
9. $$6x^2-8x=0$$
10. $$7x^2-20x=0$$
11. $$-x^2+22x=0$$
12. $$4x^2+22x=0$$

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

##### Verbetersleutel

1. $$-4x^2-20x=0 \\ \Leftrightarrow x(-4x-20) = 0 \\ \Leftrightarrow x = 0 \vee -4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-4} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------$$
2. $$8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------$$
3. $$3x^2-7x=0 \\ \Leftrightarrow x(3x-7) = 0 \\ \Leftrightarrow x = 0 \vee 3x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------$$
4. $$-5(-6x^2+3x)=-(-33x^2+25x) \\ \Leftrightarrow 30x^2-15x=33x^2-25x \\ \Leftrightarrow 30x^2-15x-33x^2+25x= 0 \\ \Leftrightarrow -3x^2-10x=0 \\ \Leftrightarrow x(-3x-10) = 0 \\ \Leftrightarrow x = 0 \vee -3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-3} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------$$
5. $$-8x^2-14x=-7x^2-10x \\ \Leftrightarrow -x^2+4x=0 \\ \Leftrightarrow x(-x+4) = 0 \\ \Leftrightarrow x = 0 \vee -x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-1} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------$$
6. $$-5(8x^2+3x)=-(42x^2+15x) \\ \Leftrightarrow -40x^2-15x=-42x^2-15x \\ \Leftrightarrow -40x^2-15x+42x^2+15x= 0 \\ \Leftrightarrow 2x^2+0x=0 \\ \Leftrightarrow 2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------$$
7. $$4(-6x^2-5x)=-(26x^2+31x) \\ \Leftrightarrow -24x^2-20x=-26x^2-31x \\ \Leftrightarrow -24x^2-20x+26x^2+31x= 0 \\ \Leftrightarrow 2x^2-11x=0 \\ \Leftrightarrow x(2x-11) = 0 \\ \Leftrightarrow x = 0 \vee 2x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------$$
8. $$4x^2+11x=0 \\ \Leftrightarrow x(4x+11) = 0 \\ \Leftrightarrow x = 0 \vee 4x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------$$
9. $$6x^2-8x=0 \\ \Leftrightarrow x(6x-8) = 0 \\ \Leftrightarrow x = 0 \vee 6x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{6} = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------$$
10. $$7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------$$
11. $$-x^2+22x=0 \\ \Leftrightarrow x(-x+22) = 0 \\ \Leftrightarrow x = 0 \vee -x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-1} = 22 \\ V = \Big\{ 22; 0 \Big\} \\ -----------------$$
12. $$4x^2+22x=0 \\ \Leftrightarrow x(4x+22) = 0 \\ \Leftrightarrow x = 0 \vee 4x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{4} = \frac{-11}{2} \\ V = \Big\{ 0 ; \frac{-11}{2} \Big\} \\ -----------------$$
Oefeningengenerator vanhoeckes.be/wiskunde 2022-06-27 08:13:48