Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(9x^2-10x=3x^2+9x\)
2. \(-2x^2-14x=-6x^2-6x\)
3. \(2x^2+17x=0\)
4. \(6x^2+22x=0\)
5. \(10x^2+14x=2x^2-10x\)
6. \(-2(2x^2-4x)=-(9x^2-x)\)
7. \(-4x^2-1x=0\)
8. \(-5x^2+13x=0\)
9. \(4(9x^2-7x)=-(-33x^2+39x)\)
10. \(-5x^2-14x=0\)
11. \(8x^2-5x=10x^2+9x\)
12. \(7x^2+8x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(9x^2-10x=3x^2+9x \\ \Leftrightarrow 6x^2-19x=0 \\ \Leftrightarrow x(6x-19) = 0 \\ \Leftrightarrow x = 0 \vee 6x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{6} \\ V = \Big\{ \frac{19}{6}; 0 \Big\} \\ -----------------\)
2. \(-2x^2-14x=-6x^2-6x \\ \Leftrightarrow 4x^2-8x=0 \\ \Leftrightarrow x(4x-8) = 0 \\ \Leftrightarrow x = 0 \vee 4x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{4} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
3. \(2x^2+17x=0 \\ \Leftrightarrow x(2x+17) = 0 \\ \Leftrightarrow x = 0 \vee 2x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
4. \(6x^2+22x=0 \\ \Leftrightarrow x(6x+22) = 0 \\ \Leftrightarrow x = 0 \vee 6x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{6} = \frac{-11}{3} \\ V = \Big\{ 0 ; \frac{-11}{3} \Big\} \\ -----------------\)
5. \(10x^2+14x=2x^2-10x \\ \Leftrightarrow 8x^2+24x=0 \\ \Leftrightarrow x(8x+24) = 0 \\ \Leftrightarrow x = 0 \vee 8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{8} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
6. \(-2(2x^2-4x)=-(9x^2-x) \\ \Leftrightarrow -4x^2+8x=-9x^2+x \\ \Leftrightarrow -4x^2+8x+9x^2-x= 0 \\ \Leftrightarrow 5x^2-7x=0 \\ \Leftrightarrow x(5x-7) = 0 \\ \Leftrightarrow x = 0 \vee 5x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{5} \\ V = \Big\{ \frac{7}{5}; 0 \Big\} \\ -----------------\)
7. \(-4x^2-1x=0 \\ \Leftrightarrow x(-4x-1) = 0 \\ \Leftrightarrow x = 0 \vee -4x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-4} = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
8. \(-5x^2+13x=0 \\ \Leftrightarrow x(-5x+13) = 0 \\ \Leftrightarrow x = 0 \vee -5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-5} = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
9. \(4(9x^2-7x)=-(-33x^2+39x) \\ \Leftrightarrow 36x^2-28x=33x^2-39x \\ \Leftrightarrow 36x^2-28x-33x^2+39x= 0 \\ \Leftrightarrow 3x^2-11x=0 \\ \Leftrightarrow x(3x-11) = 0 \\ \Leftrightarrow x = 0 \vee 3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
10. \(-5x^2-14x=0 \\ \Leftrightarrow x(-5x-14) = 0 \\ \Leftrightarrow x = 0 \vee -5x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-5} = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
11. \(8x^2-5x=10x^2+9x \\ \Leftrightarrow -2x^2-14x=0 \\ \Leftrightarrow x(-2x-14) = 0 \\ \Leftrightarrow x = 0 \vee -2x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-2} = -7 \\ V = \Big\{ 0 ; -7 \Big\} \\ -----------------\)
12. \(7x^2+8x=0 \\ \Leftrightarrow x(7x+8) = 0 \\ \Leftrightarrow x = 0 \vee 7x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{7} \\ V = \Big\{ 0 ; \frac{-8}{7} \Big\} \\ -----------------\)