Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-9x^2+2x)=-(23x^2-12x)\)
2. \(2x^2-7x=7x^2+6x\)
3. \(6x^2+23x=0\)
4. \(-2(2x^2-8x)=-(5x^2-32x)\)
5. \(3x^2+10x=0\)
6. \(-7x^2+19x=0\)
7. \(-5x^2-x=2x^2-5x\)
8. \(4x^2-27x=-3x^2-7x\)
9. \(-5x^2+15x=0\)
10. \(-7x^2+18x=0\)
11. \(-12x^2-22x=-4x^2-7x\)
12. \(-x^2+4x=-3x^2-3x\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-9x^2+2x)=-(23x^2-12x) \\ \Leftrightarrow -18x^2+4x=-23x^2+12x \\ \Leftrightarrow -18x^2+4x+23x^2-12x= 0 \\ \Leftrightarrow 5x^2+8x=0 \\ \Leftrightarrow x(5x+8) = 0 \\ \Leftrightarrow x = 0 \vee 5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{5} \\ V = \Big\{ 0 ; \frac{-8}{5} \Big\} \\ -----------------\)
2. \(2x^2-7x=7x^2+6x \\ \Leftrightarrow -5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
3. \(6x^2+23x=0 \\ \Leftrightarrow x(6x+23) = 0 \\ \Leftrightarrow x = 0 \vee 6x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
4. \(-2(2x^2-8x)=-(5x^2-32x) \\ \Leftrightarrow -4x^2+16x=-5x^2+32x \\ \Leftrightarrow -4x^2+16x+5x^2-32x= 0 \\ \Leftrightarrow x^2+16x=0 \\ \Leftrightarrow x(x+16) = 0 \\ \Leftrightarrow x = 0 \vee x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{1} = -16 \\ V = \Big\{ 0 ; -16 \Big\} \\ -----------------\)
5. \(3x^2+10x=0 \\ \Leftrightarrow x(3x+10) = 0 \\ \Leftrightarrow x = 0 \vee 3x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
6. \(-7x^2+19x=0 \\ \Leftrightarrow x(-7x+19) = 0 \\ \Leftrightarrow x = 0 \vee -7x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-7} = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
7. \(-5x^2-x=2x^2-5x \\ \Leftrightarrow -7x^2+4x=0 \\ \Leftrightarrow x(-7x+4) = 0 \\ \Leftrightarrow x = 0 \vee -7x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-7} = \frac{4}{7} \\ V = \Big\{ \frac{4}{7}; 0 \Big\} \\ -----------------\)
8. \(4x^2-27x=-3x^2-7x \\ \Leftrightarrow 7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------\)
9. \(-5x^2+15x=0 \\ \Leftrightarrow x(-5x+15) = 0 \\ \Leftrightarrow x = 0 \vee -5x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(-7x^2+18x=0 \\ \Leftrightarrow x(-7x+18) = 0 \\ \Leftrightarrow x = 0 \vee -7x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-7} = \frac{18}{7} \\ V = \Big\{ \frac{18}{7}; 0 \Big\} \\ -----------------\)
11. \(-12x^2-22x=-4x^2-7x \\ \Leftrightarrow -8x^2-15x=0 \\ \Leftrightarrow x(-8x-15) = 0 \\ \Leftrightarrow x = 0 \vee -8x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-8} = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)
12. \(-x^2+4x=-3x^2-3x \\ \Leftrightarrow 2x^2+7x=0 \\ \Leftrightarrow x(2x+7) = 0 \\ \Leftrightarrow x = 0 \vee 2x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)