Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-4x^2+10x)=-(0x^2-41x)\)
2. \(2x^2-4x=0\)
3. \(-2x^2-23x=-8x^2+2x\)
4. \(-2(-6x^2+3x)=-(-19x^2+6x)\)
5. \(-3x^2+3x=5x^2-10x\)
6. \(x^2+2x=0\)
7. \(-2(4x^2-2x)=-(6x^2-11x)\)
8. \(-4x^2-7x=0\)
9. \(5(7x^2-6x)=-(-29x^2+51x)\)
10. \(2x^2+17x=0\)
11. \(-5(3x^2-8x)=-(22x^2-61x)\)
12. \(5x^2+20x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-4x^2+10x)=-(0x^2-41x) \\ \Leftrightarrow -8x^2+20x=0x^2+41x \\ \Leftrightarrow -8x^2+20x+0x^2-41x= 0 \\ \Leftrightarrow -8x^2+21x=0 \\ \Leftrightarrow x(-8x+21) = 0 \\ \Leftrightarrow x = 0 \vee -8x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{-8} = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
2. \(2x^2-4x=0 \\ \Leftrightarrow x(2x-4) = 0 \\ \Leftrightarrow x = 0 \vee 2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{2} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
3. \(-2x^2-23x=-8x^2+2x \\ \Leftrightarrow 6x^2-25x=0 \\ \Leftrightarrow x(6x-25) = 0 \\ \Leftrightarrow x = 0 \vee 6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{6} \\ V = \Big\{ \frac{25}{6}; 0 \Big\} \\ -----------------\)
4. \(-2(-6x^2+3x)=-(-19x^2+6x) \\ \Leftrightarrow 12x^2-6x=19x^2-6x \\ \Leftrightarrow 12x^2-6x-19x^2+6x= 0 \\ \Leftrightarrow -7x^2+0x=0 \\ \Leftrightarrow -7x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-7} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-3x^2+3x=5x^2-10x \\ \Leftrightarrow -8x^2+13x=0 \\ \Leftrightarrow x(-8x+13) = 0 \\ \Leftrightarrow x = 0 \vee -8x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-8} = \frac{13}{8} \\ V = \Big\{ \frac{13}{8}; 0 \Big\} \\ -----------------\)
6. \(x^2+2x=0 \\ \Leftrightarrow x(x+2) = 0 \\ \Leftrightarrow x = 0 \vee x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{1} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
7. \(-2(4x^2-2x)=-(6x^2-11x) \\ \Leftrightarrow -8x^2+4x=-6x^2+11x \\ \Leftrightarrow -8x^2+4x+6x^2-11x= 0 \\ \Leftrightarrow -2x^2+7x=0 \\ \Leftrightarrow x(-2x+7) = 0 \\ \Leftrightarrow x = 0 \vee -2x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-2} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
8. \(-4x^2-7x=0 \\ \Leftrightarrow x(-4x-7) = 0 \\ \Leftrightarrow x = 0 \vee -4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-4} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
9. \(5(7x^2-6x)=-(-29x^2+51x) \\ \Leftrightarrow 35x^2-30x=29x^2-51x \\ \Leftrightarrow 35x^2-30x-29x^2+51x= 0 \\ \Leftrightarrow 6x^2-21x=0 \\ \Leftrightarrow x(6x-21) = 0 \\ \Leftrightarrow x = 0 \vee 6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{6} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
10. \(2x^2+17x=0 \\ \Leftrightarrow x(2x+17) = 0 \\ \Leftrightarrow x = 0 \vee 2x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{2} \\ V = \Big\{ 0 ; \frac{-17}{2} \Big\} \\ -----------------\)
11. \(-5(3x^2-8x)=-(22x^2-61x) \\ \Leftrightarrow -15x^2+40x=-22x^2+61x \\ \Leftrightarrow -15x^2+40x+22x^2-61x= 0 \\ \Leftrightarrow 7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(5x^2+20x=0 \\ \Leftrightarrow x(5x+20) = 0 \\ \Leftrightarrow x = 0 \vee 5x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)