Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+7x=0\)
2. \(2x^2+x=6x^2-4x\)
3. \(3x^2+6x=0\)
4. \(-2(10x^2-3x)=-(25x^2-10x)\)
5. \(5x^2+10x=-2x^2+4x\)
6. \(-6x^2-25x=0\)
7. \(-5x^2+2x=0\)
8. \(3x^2+5x=0\)
9. \(11x^2+19x=6x^2+8x\)
10. \(2x^2-17x=10x^2-4x\)
11. \(2x^2-6x=0\)
12. \(5(9x^2-2x)=-(-52x^2+3x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+7x=0 \\ \Leftrightarrow x(-4x+7) = 0 \\ \Leftrightarrow x = 0 \vee -4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-4} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
2. \(2x^2+x=6x^2-4x \\ \Leftrightarrow -4x^2+5x=0 \\ \Leftrightarrow x(-4x+5) = 0 \\ \Leftrightarrow x = 0 \vee -4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-4} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
3. \(3x^2+6x=0 \\ \Leftrightarrow x(3x+6) = 0 \\ \Leftrightarrow x = 0 \vee 3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{3} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
4. \(-2(10x^2-3x)=-(25x^2-10x) \\ \Leftrightarrow -20x^2+6x=-25x^2+10x \\ \Leftrightarrow -20x^2+6x+25x^2-10x= 0 \\ \Leftrightarrow 5x^2+4x=0 \\ \Leftrightarrow x(5x+4) = 0 \\ \Leftrightarrow x = 0 \vee 5x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{5} \\ V = \Big\{ 0 ; \frac{-4}{5} \Big\} \\ -----------------\)
5. \(5x^2+10x=-2x^2+4x \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
6. \(-6x^2-25x=0 \\ \Leftrightarrow x(-6x-25) = 0 \\ \Leftrightarrow x = 0 \vee -6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{-6} = \frac{-25}{6} \\ V = \Big\{ 0 ; \frac{-25}{6} \Big\} \\ -----------------\)
7. \(-5x^2+2x=0 \\ \Leftrightarrow x(-5x+2) = 0 \\ \Leftrightarrow x = 0 \vee -5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-5} = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
8. \(3x^2+5x=0 \\ \Leftrightarrow x(3x+5) = 0 \\ \Leftrightarrow x = 0 \vee 3x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
9. \(11x^2+19x=6x^2+8x \\ \Leftrightarrow 5x^2+11x=0 \\ \Leftrightarrow x(5x+11) = 0 \\ \Leftrightarrow x = 0 \vee 5x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{5} \\ V = \Big\{ 0 ; \frac{-11}{5} \Big\} \\ -----------------\)
10. \(2x^2-17x=10x^2-4x \\ \Leftrightarrow -8x^2-13x=0 \\ \Leftrightarrow x(-8x-13) = 0 \\ \Leftrightarrow x = 0 \vee -8x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-8} = \frac{-13}{8} \\ V = \Big\{ 0 ; \frac{-13}{8} \Big\} \\ -----------------\)
11. \(2x^2-6x=0 \\ \Leftrightarrow x(2x-6) = 0 \\ \Leftrightarrow x = 0 \vee 2x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{2} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
12. \(5(9x^2-2x)=-(-52x^2+3x) \\ \Leftrightarrow 45x^2-10x=52x^2-3x \\ \Leftrightarrow 45x^2-10x-52x^2+3x= 0 \\ \Leftrightarrow -7x^2+7x=0 \\ \Leftrightarrow x(-7x+7) = 0 \\ \Leftrightarrow x = 0 \vee -7x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-7} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)