Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2+8x=0\)
2. \(8x^2+12x=0\)
3. \(2(-10x^2+5x)=-(13x^2-25x)\)
4. \(-15x^2+11x=-10x^2-8x\)
5. \(13x^2-17x=10x^2-7x\)
6. \(-8x^2-3x=0\)
7. \(-3x^2+25x=0\)
8. \(6x^2-4x=0\)
9. \(-13x^2+19x=-10x^2-3x\)
10. \(2x^2-7x=0\)
11. \(-4(6x^2+10x)=-(25x^2+48x)\)
12. \(-10x^2-27x=-9x^2-4x\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2+8x=0 \\ \Leftrightarrow x(3x+8) = 0 \\ \Leftrightarrow x = 0 \vee 3x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
2. \(8x^2+12x=0 \\ \Leftrightarrow x(8x+12) = 0 \\ \Leftrightarrow x = 0 \vee 8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
3. \(2(-10x^2+5x)=-(13x^2-25x) \\ \Leftrightarrow -20x^2+10x=-13x^2+25x \\ \Leftrightarrow -20x^2+10x+13x^2-25x= 0 \\ \Leftrightarrow -7x^2+15x=0 \\ \Leftrightarrow x(-7x+15) = 0 \\ \Leftrightarrow x = 0 \vee -7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-7} = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)
4. \(-15x^2+11x=-10x^2-8x \\ \Leftrightarrow -5x^2+19x=0 \\ \Leftrightarrow x(-5x+19) = 0 \\ \Leftrightarrow x = 0 \vee -5x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-5} = \frac{19}{5} \\ V = \Big\{ \frac{19}{5}; 0 \Big\} \\ -----------------\)
5. \(13x^2-17x=10x^2-7x \\ \Leftrightarrow 3x^2-10x=0 \\ \Leftrightarrow x(3x-10) = 0 \\ \Leftrightarrow x = 0 \vee 3x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{3} \\ V = \Big\{ \frac{10}{3}; 0 \Big\} \\ -----------------\)
6. \(-8x^2-3x=0 \\ \Leftrightarrow x(-8x-3) = 0 \\ \Leftrightarrow x = 0 \vee -8x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-8} = \frac{-3}{8} \\ V = \Big\{ 0 ; \frac{-3}{8} \Big\} \\ -----------------\)
7. \(-3x^2+25x=0 \\ \Leftrightarrow x(-3x+25) = 0 \\ \Leftrightarrow x = 0 \vee -3x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-3} = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)
8. \(6x^2-4x=0 \\ \Leftrightarrow x(6x-4) = 0 \\ \Leftrightarrow x = 0 \vee 6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
9. \(-13x^2+19x=-10x^2-3x \\ \Leftrightarrow -3x^2+22x=0 \\ \Leftrightarrow x(-3x+22) = 0 \\ \Leftrightarrow x = 0 \vee -3x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-3} = \frac{22}{3} \\ V = \Big\{ \frac{22}{3}; 0 \Big\} \\ -----------------\)
10. \(2x^2-7x=0 \\ \Leftrightarrow x(2x-7) = 0 \\ \Leftrightarrow x = 0 \vee 2x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
11. \(-4(6x^2+10x)=-(25x^2+48x) \\ \Leftrightarrow -24x^2-40x=-25x^2-48x \\ \Leftrightarrow -24x^2-40x+25x^2+48x= 0 \\ \Leftrightarrow x^2-8x=0 \\ \Leftrightarrow x(x-8) = 0 \\ \Leftrightarrow x = 0 \vee x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
12. \(-10x^2-27x=-9x^2-4x \\ \Leftrightarrow -x^2-23x=0 \\ \Leftrightarrow x(-x-23) = 0 \\ \Leftrightarrow x = 0 \vee -x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)