Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(15x^2-6x=7x^2+2x\)
2. \(-3x^2+20x=0\)
3. \(-11x^2+16x=-3x^2+6x\)
4. \(2(-2x^2-4x)=-(x^2-4x)\)
5. \(2x^2-6x=0\)
6. \(-5(-2x^2+3x)=-(-4x^2-x)\)
7. \(-3x^2-5x=5x^2+9x\)
8. \(-5x^2-13x=0\)
9. \(-3(-7x^2-5x)=-(-22x^2-39x)\)
10. \(7x^2-6x=0\)
11. \(4x^2-9x=0\)
12. \(12x^2-17x=8x^2+8x\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(15x^2-6x=7x^2+2x \\ \Leftrightarrow 8x^2-8x=0 \\ \Leftrightarrow x(8x-8) = 0 \\ \Leftrightarrow x = 0 \vee 8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{8} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(-3x^2+20x=0 \\ \Leftrightarrow x(-3x+20) = 0 \\ \Leftrightarrow x = 0 \vee -3x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-3} = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)
3. \(-11x^2+16x=-3x^2+6x \\ \Leftrightarrow -8x^2+10x=0 \\ \Leftrightarrow x(-8x+10) = 0 \\ \Leftrightarrow x = 0 \vee -8x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-8} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
4. \(2(-2x^2-4x)=-(x^2-4x) \\ \Leftrightarrow -4x^2-8x=-x^2+4x \\ \Leftrightarrow -4x^2-8x+x^2-4x= 0 \\ \Leftrightarrow -3x^2+12x=0 \\ \Leftrightarrow x(-3x+12) = 0 \\ \Leftrightarrow x = 0 \vee -3x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-3} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
5. \(2x^2-6x=0 \\ \Leftrightarrow x(2x-6) = 0 \\ \Leftrightarrow x = 0 \vee 2x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{2} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
6. \(-5(-2x^2+3x)=-(-4x^2-x) \\ \Leftrightarrow 10x^2-15x=4x^2+x \\ \Leftrightarrow 10x^2-15x-4x^2-x= 0 \\ \Leftrightarrow 6x^2+16x=0 \\ \Leftrightarrow x(6x+16) = 0 \\ \Leftrightarrow x = 0 \vee 6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{6} = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
7. \(-3x^2-5x=5x^2+9x \\ \Leftrightarrow -8x^2-14x=0 \\ \Leftrightarrow x(-8x-14) = 0 \\ \Leftrightarrow x = 0 \vee -8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-8} = \frac{-7}{4} \\ V = \Big\{ 0 ; \frac{-7}{4} \Big\} \\ -----------------\)
8. \(-5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
9. \(-3(-7x^2-5x)=-(-22x^2-39x) \\ \Leftrightarrow 21x^2+15x=22x^2+39x \\ \Leftrightarrow 21x^2+15x-22x^2-39x= 0 \\ \Leftrightarrow -x^2+24x=0 \\ \Leftrightarrow x(-x+24) = 0 \\ \Leftrightarrow x = 0 \vee -x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-1} = 24 \\ V = \Big\{ 24; 0 \Big\} \\ -----------------\)
10. \(7x^2-6x=0 \\ \Leftrightarrow x(7x-6) = 0 \\ \Leftrightarrow x = 0 \vee 7x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{7} \\ V = \Big\{ \frac{6}{7}; 0 \Big\} \\ -----------------\)
11. \(4x^2-9x=0 \\ \Leftrightarrow x(4x-9) = 0 \\ \Leftrightarrow x = 0 \vee 4x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
12. \(12x^2-17x=8x^2+8x \\ \Leftrightarrow 4x^2-25x=0 \\ \Leftrightarrow x(4x-25) = 0 \\ \Leftrightarrow x = 0 \vee 4x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{4} \\ V = \Big\{ \frac{25}{4}; 0 \Big\} \\ -----------------\)