Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+10x=0\)
2. \(-6x^2-11x=-4x^2-3x\)
3. \(12x^2+13x=4x^2+9x\)
4. \(7x^2+3x=8x^2-5x\)
5. \(-2x^2+8x=-8x^2+2x\)
6. \(8x^2+11x=0\)
7. \(x^2+9x=0\)
8. \(-5(4x^2+3x)=-(15x^2-9x)\)
9. \(-8x^2-5x=0\)
10. \(-8x^2-10x=-6x^2-6x\)
11. \(-4(-6x^2+3x)=-(-31x^2+16x)\)
12. \(-2(3x^2-6x)=-(7x^2-35x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+10x=0 \\ \Leftrightarrow x(8x+10) = 0 \\ \Leftrightarrow x = 0 \vee 8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{8} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
2. \(-6x^2-11x=-4x^2-3x \\ \Leftrightarrow -2x^2-8x=0 \\ \Leftrightarrow x(-2x-8) = 0 \\ \Leftrightarrow x = 0 \vee -2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-2} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
3. \(12x^2+13x=4x^2+9x \\ \Leftrightarrow 8x^2+4x=0 \\ \Leftrightarrow x(8x+4) = 0 \\ \Leftrightarrow x = 0 \vee 8x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{8} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
4. \(7x^2+3x=8x^2-5x \\ \Leftrightarrow -x^2+8x=0 \\ \Leftrightarrow x(-x+8) = 0 \\ \Leftrightarrow x = 0 \vee -x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-1} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
5. \(-2x^2+8x=-8x^2+2x \\ \Leftrightarrow 6x^2+6x=0 \\ \Leftrightarrow x(6x+6) = 0 \\ \Leftrightarrow x = 0 \vee 6x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{6} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
6. \(8x^2+11x=0 \\ \Leftrightarrow x(8x+11) = 0 \\ \Leftrightarrow x = 0 \vee 8x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{8} \\ V = \Big\{ 0 ; \frac{-11}{8} \Big\} \\ -----------------\)
7. \(x^2+9x=0 \\ \Leftrightarrow x(x+9) = 0 \\ \Leftrightarrow x = 0 \vee x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{1} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
8. \(-5(4x^2+3x)=-(15x^2-9x) \\ \Leftrightarrow -20x^2-15x=-15x^2+9x \\ \Leftrightarrow -20x^2-15x+15x^2-9x= 0 \\ \Leftrightarrow -5x^2+24x=0 \\ \Leftrightarrow x(-5x+24) = 0 \\ \Leftrightarrow x = 0 \vee -5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-5} = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
9. \(-8x^2-5x=0 \\ \Leftrightarrow x(-8x-5) = 0 \\ \Leftrightarrow x = 0 \vee -8x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-8} = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
10. \(-8x^2-10x=-6x^2-6x \\ \Leftrightarrow -2x^2-4x=0 \\ \Leftrightarrow x(-2x-4) = 0 \\ \Leftrightarrow x = 0 \vee -2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-2} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
11. \(-4(-6x^2+3x)=-(-31x^2+16x) \\ \Leftrightarrow 24x^2-12x=31x^2-16x \\ \Leftrightarrow 24x^2-12x-31x^2+16x= 0 \\ \Leftrightarrow -7x^2-4x=0 \\ \Leftrightarrow x(-7x-4) = 0 \\ \Leftrightarrow x = 0 \vee -7x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-7} = \frac{-4}{7} \\ V = \Big\{ 0 ; \frac{-4}{7} \Big\} \\ -----------------\)
12. \(-2(3x^2-6x)=-(7x^2-35x) \\ \Leftrightarrow -6x^2+12x=-7x^2+35x \\ \Leftrightarrow -6x^2+12x+7x^2-35x= 0 \\ \Leftrightarrow x^2+23x=0 \\ \Leftrightarrow x(x+23) = 0 \\ \Leftrightarrow x = 0 \vee x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{1} = -23 \\ V = \Big\{ 0 ; -23 \Big\} \\ -----------------\)