Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(-5x^2+5x)=-(23x^2-15x)\)
2. \(-14x^2-2x=-10x^2-2x\)
3. \(-12x^2-17x=-7x^2+3x\)
4. \(2(9x^2+5x)=-(-12x^2-23x)\)
5. \(8x^2-19x=0\)
6. \(-8x^2+25x=0\)
7. \(x^2+0x=0\)
8. \(13x^2-15x=5x^2-4x\)
9. \(4(-3x^2-9x)=-(11x^2+33x)\)
10. \(-3x^2-2x=-7x^2+7x\)
11. \(2(4x^2-8x)=-(-14x^2+16x)\)
12. \(5(-10x^2-10x)=-(43x^2+48x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(-5x^2+5x)=-(23x^2-15x) \\ \Leftrightarrow -25x^2+25x=-23x^2+15x \\ \Leftrightarrow -25x^2+25x+23x^2-15x= 0 \\ \Leftrightarrow -2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
2. \(-14x^2-2x=-10x^2-2x \\ \Leftrightarrow -4x^2+0x=0 \\ \Leftrightarrow -4x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-4} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-12x^2-17x=-7x^2+3x \\ \Leftrightarrow -5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
4. \(2(9x^2+5x)=-(-12x^2-23x) \\ \Leftrightarrow 18x^2+10x=12x^2+23x \\ \Leftrightarrow 18x^2+10x-12x^2-23x= 0 \\ \Leftrightarrow 6x^2+13x=0 \\ \Leftrightarrow x(6x+13) = 0 \\ \Leftrightarrow x = 0 \vee 6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
5. \(8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------\)
6. \(-8x^2+25x=0 \\ \Leftrightarrow x(-8x+25) = 0 \\ \Leftrightarrow x = 0 \vee -8x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-8} = \frac{25}{8} \\ V = \Big\{ \frac{25}{8}; 0 \Big\} \\ -----------------\)
7. \(x^2+0x=0 \\ \Leftrightarrow x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{1} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(13x^2-15x=5x^2-4x \\ \Leftrightarrow 8x^2-11x=0 \\ \Leftrightarrow x(8x-11) = 0 \\ \Leftrightarrow x = 0 \vee 8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
9. \(4(-3x^2-9x)=-(11x^2+33x) \\ \Leftrightarrow -12x^2-36x=-11x^2-33x \\ \Leftrightarrow -12x^2-36x+11x^2+33x= 0 \\ \Leftrightarrow -x^2+3x=0 \\ \Leftrightarrow x(-x+3) = 0 \\ \Leftrightarrow x = 0 \vee -x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
10. \(-3x^2-2x=-7x^2+7x \\ \Leftrightarrow 4x^2-9x=0 \\ \Leftrightarrow x(4x-9) = 0 \\ \Leftrightarrow x = 0 \vee 4x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
11. \(2(4x^2-8x)=-(-14x^2+16x) \\ \Leftrightarrow 8x^2-16x=14x^2-16x \\ \Leftrightarrow 8x^2-16x-14x^2+16x= 0 \\ \Leftrightarrow -6x^2+0x=0 \\ \Leftrightarrow -6x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-6} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(-10x^2-10x)=-(43x^2+48x) \\ \Leftrightarrow -50x^2-50x=-43x^2-48x \\ \Leftrightarrow -50x^2-50x+43x^2+48x= 0 \\ \Leftrightarrow -7x^2+2x=0 \\ \Leftrightarrow x(-7x+2) = 0 \\ \Leftrightarrow x = 0 \vee -7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-7} = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)