Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2-8x=-9x^2+6x\)
2. \(-10x^2-26x=-2x^2-8x\)
3. \(-4(8x^2+8x)=-(36x^2+36x)\)
4. \(3x^2-3x=-4x^2+9x\)
5. \(-x^2-29x=-6x^2-6x\)
6. \(-7x^2+11x=0\)
7. \(5x^2-25x=0\)
8. \(-5x^2-2x=-7x^2-10x\)
9. \(4x^2+8x=5x^2-5x\)
10. \(x^2+8x=7x^2+8x\)
11. \(5x^2-13x=0\)
12. \(-3(-9x^2+8x)=-(-21x^2+26x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2-8x=-9x^2+6x \\ \Leftrightarrow -4x^2-14x=0 \\ \Leftrightarrow x(-4x-14) = 0 \\ \Leftrightarrow x = 0 \vee -4x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-4} = \frac{-7}{2} \\ V = \Big\{ 0 ; \frac{-7}{2} \Big\} \\ -----------------\)
2. \(-10x^2-26x=-2x^2-8x \\ \Leftrightarrow -8x^2-18x=0 \\ \Leftrightarrow x(-8x-18) = 0 \\ \Leftrightarrow x = 0 \vee -8x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-8} = \frac{-9}{4} \\ V = \Big\{ 0 ; \frac{-9}{4} \Big\} \\ -----------------\)
3. \(-4(8x^2+8x)=-(36x^2+36x) \\ \Leftrightarrow -32x^2-32x=-36x^2-36x \\ \Leftrightarrow -32x^2-32x+36x^2+36x= 0 \\ \Leftrightarrow 4x^2-4x=0 \\ \Leftrightarrow x(4x-4) = 0 \\ \Leftrightarrow x = 0 \vee 4x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{4} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
4. \(3x^2-3x=-4x^2+9x \\ \Leftrightarrow 7x^2-12x=0 \\ \Leftrightarrow x(7x-12) = 0 \\ \Leftrightarrow x = 0 \vee 7x-12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{12}{7} \\ V = \Big\{ \frac{12}{7}; 0 \Big\} \\ -----------------\)
5. \(-x^2-29x=-6x^2-6x \\ \Leftrightarrow 5x^2-23x=0 \\ \Leftrightarrow x(5x-23) = 0 \\ \Leftrightarrow x = 0 \vee 5x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
6. \(-7x^2+11x=0 \\ \Leftrightarrow x(-7x+11) = 0 \\ \Leftrightarrow x = 0 \vee -7x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-7} = \frac{11}{7} \\ V = \Big\{ \frac{11}{7}; 0 \Big\} \\ -----------------\)
7. \(5x^2-25x=0 \\ \Leftrightarrow x(5x-25) = 0 \\ \Leftrightarrow x = 0 \vee 5x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{5} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
8. \(-5x^2-2x=-7x^2-10x \\ \Leftrightarrow 2x^2+8x=0 \\ \Leftrightarrow x(2x+8) = 0 \\ \Leftrightarrow x = 0 \vee 2x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
9. \(4x^2+8x=5x^2-5x \\ \Leftrightarrow -x^2+13x=0 \\ \Leftrightarrow x(-x+13) = 0 \\ \Leftrightarrow x = 0 \vee -x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-1} = 13 \\ V = \Big\{ 13; 0 \Big\} \\ -----------------\)
10. \(x^2+8x=7x^2+8x \\ \Leftrightarrow -6x^2+0x=0 \\ \Leftrightarrow -6x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-6} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(5x^2-13x=0 \\ \Leftrightarrow x(5x-13) = 0 \\ \Leftrightarrow x = 0 \vee 5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{5} \\ V = \Big\{ \frac{13}{5}; 0 \Big\} \\ -----------------\)
12. \(-3(-9x^2+8x)=-(-21x^2+26x) \\ \Leftrightarrow 27x^2-24x=21x^2-26x \\ \Leftrightarrow 27x^2-24x-21x^2+26x= 0 \\ \Leftrightarrow 6x^2-2x=0 \\ \Leftrightarrow x(6x-2) = 0 \\ \Leftrightarrow x = 0 \vee 6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{6} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)