Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+8x=0\)
2. \(-5(3x^2+7x)=-(23x^2+57x)\)
3. \(6x^2-22x=0\)
4. \(-4x^2+23x=-3x^2+10x\)
5. \(3(8x^2+10x)=-(-28x^2-33x)\)
6. \(-4x^2+23x=0\)
7. \(x^2+20x=0\)
8. \(-4(7x^2+6x)=-(30x^2+5x)\)
9. \(-2x^2+18x=5x^2-7x\)
10. \(-5(-3x^2+6x)=-(-13x^2+29x)\)
11. \(-16x^2-8x=-9x^2+3x\)
12. \(-3x^2+11x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+8x=0 \\ \Leftrightarrow x(-5x+8) = 0 \\ \Leftrightarrow x = 0 \vee -5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-5} = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
2. \(-5(3x^2+7x)=-(23x^2+57x) \\ \Leftrightarrow -15x^2-35x=-23x^2-57x \\ \Leftrightarrow -15x^2-35x+23x^2+57x= 0 \\ \Leftrightarrow 8x^2-22x=0 \\ \Leftrightarrow x(8x-22) = 0 \\ \Leftrightarrow x = 0 \vee 8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{8} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
3. \(6x^2-22x=0 \\ \Leftrightarrow x(6x-22) = 0 \\ \Leftrightarrow x = 0 \vee 6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
4. \(-4x^2+23x=-3x^2+10x \\ \Leftrightarrow -x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
5. \(3(8x^2+10x)=-(-28x^2-33x) \\ \Leftrightarrow 24x^2+30x=28x^2+33x \\ \Leftrightarrow 24x^2+30x-28x^2-33x= 0 \\ \Leftrightarrow -4x^2+3x=0 \\ \Leftrightarrow x(-4x+3) = 0 \\ \Leftrightarrow x = 0 \vee -4x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-4} = \frac{3}{4} \\ V = \Big\{ \frac{3}{4}; 0 \Big\} \\ -----------------\)
6. \(-4x^2+23x=0 \\ \Leftrightarrow x(-4x+23) = 0 \\ \Leftrightarrow x = 0 \vee -4x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-4} = \frac{23}{4} \\ V = \Big\{ \frac{23}{4}; 0 \Big\} \\ -----------------\)
7. \(x^2+20x=0 \\ \Leftrightarrow x(x+20) = 0 \\ \Leftrightarrow x = 0 \vee x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{1} = -20 \\ V = \Big\{ 0 ; -20 \Big\} \\ -----------------\)
8. \(-4(7x^2+6x)=-(30x^2+5x) \\ \Leftrightarrow -28x^2-24x=-30x^2-5x \\ \Leftrightarrow -28x^2-24x+30x^2+5x= 0 \\ \Leftrightarrow 2x^2+19x=0 \\ \Leftrightarrow x(2x+19) = 0 \\ \Leftrightarrow x = 0 \vee 2x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{2} \\ V = \Big\{ 0 ; \frac{-19}{2} \Big\} \\ -----------------\)
9. \(-2x^2+18x=5x^2-7x \\ \Leftrightarrow -7x^2+25x=0 \\ \Leftrightarrow x(-7x+25) = 0 \\ \Leftrightarrow x = 0 \vee -7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-7} = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
10. \(-5(-3x^2+6x)=-(-13x^2+29x) \\ \Leftrightarrow 15x^2-30x=13x^2-29x \\ \Leftrightarrow 15x^2-30x-13x^2+29x= 0 \\ \Leftrightarrow 2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
11. \(-16x^2-8x=-9x^2+3x \\ \Leftrightarrow -7x^2-11x=0 \\ \Leftrightarrow x(-7x-11) = 0 \\ \Leftrightarrow x = 0 \vee -7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
12. \(-3x^2+11x=0 \\ \Leftrightarrow x(-3x+11) = 0 \\ \Leftrightarrow x = 0 \vee -3x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-3} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)