Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+4x=-8x^2+3x\)
2. \(-3(-10x^2-2x)=-(-31x^2+16x)\)
3. \(2(5x^2-4x)=-(-3x^2-2x)\)
4. \(-5x^2+23x=0\)
5. \(3x^2+18x=0\)
6. \(-4x^2+22x=0\)
7. \(5x^2+1x=0\)
8. \(-4(7x^2-4x)=-(25x^2+4x)\)
9. \(-11x^2+2x=-9x^2-9x\)
10. \(3x^2-19x=0\)
11. \(-6x^2+14x=0\)
12. \(-6x^2+11x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+4x=-8x^2+3x \\ \Leftrightarrow 2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
2. \(-3(-10x^2-2x)=-(-31x^2+16x) \\ \Leftrightarrow 30x^2+6x=31x^2-16x \\ \Leftrightarrow 30x^2+6x-31x^2+16x= 0 \\ \Leftrightarrow -x^2-22x=0 \\ \Leftrightarrow x(-x-22) = 0 \\ \Leftrightarrow x = 0 \vee -x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-1} = -22 \\ V = \Big\{ 0 ; -22 \Big\} \\ -----------------\)
3. \(2(5x^2-4x)=-(-3x^2-2x) \\ \Leftrightarrow 10x^2-8x=3x^2+2x \\ \Leftrightarrow 10x^2-8x-3x^2-2x= 0 \\ \Leftrightarrow 7x^2+10x=0 \\ \Leftrightarrow x(7x+10) = 0 \\ \Leftrightarrow x = 0 \vee 7x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)
4. \(-5x^2+23x=0 \\ \Leftrightarrow x(-5x+23) = 0 \\ \Leftrightarrow x = 0 \vee -5x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-5} = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
5. \(3x^2+18x=0 \\ \Leftrightarrow x(3x+18) = 0 \\ \Leftrightarrow x = 0 \vee 3x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{3} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
6. \(-4x^2+22x=0 \\ \Leftrightarrow x(-4x+22) = 0 \\ \Leftrightarrow x = 0 \vee -4x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-4} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
7. \(5x^2+1x=0 \\ \Leftrightarrow x(5x+1) = 0 \\ \Leftrightarrow x = 0 \vee 5x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{5} \\ V = \Big\{ 0 ; \frac{-1}{5} \Big\} \\ -----------------\)
8. \(-4(7x^2-4x)=-(25x^2+4x) \\ \Leftrightarrow -28x^2+16x=-25x^2-4x \\ \Leftrightarrow -28x^2+16x+25x^2+4x= 0 \\ \Leftrightarrow -3x^2-20x=0 \\ \Leftrightarrow x(-3x-20) = 0 \\ \Leftrightarrow x = 0 \vee -3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-3} = \frac{-20}{3} \\ V = \Big\{ 0 ; \frac{-20}{3} \Big\} \\ -----------------\)
9. \(-11x^2+2x=-9x^2-9x \\ \Leftrightarrow -2x^2+11x=0 \\ \Leftrightarrow x(-2x+11) = 0 \\ \Leftrightarrow x = 0 \vee -2x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-2} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
10. \(3x^2-19x=0 \\ \Leftrightarrow x(3x-19) = 0 \\ \Leftrightarrow x = 0 \vee 3x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{3} \\ V = \Big\{ \frac{19}{3}; 0 \Big\} \\ -----------------\)
11. \(-6x^2+14x=0 \\ \Leftrightarrow x(-6x+14) = 0 \\ \Leftrightarrow x = 0 \vee -6x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
12. \(-6x^2+11x=0 \\ \Leftrightarrow x(-6x+11) = 0 \\ \Leftrightarrow x = 0 \vee -6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-6} = \frac{11}{6} \\ V = \Big\{ \frac{11}{6}; 0 \Big\} \\ -----------------\)