Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(6x^2+11x=9x^2+5x\)
2. \(7x^2+22x=0\)
3. \(-x^2-22x=0\)
4. \(5x^2-10x=0\)
5. \(8x^2-10x=0\)
6. \(-2x^2+17x=-8x^2-7x\)
7. \(-2(-10x^2+9x)=-(-18x^2+40x)\)
8. \(18x^2-3x=10x^2-8x\)
9. \(-3(5x^2+10x)=-(22x^2+24x)\)
10. \(5x^2+10x=-2x^2-8x\)
11. \(-3(-9x^2+7x)=-(-20x^2+0x)\)
12. \(-6x^2-7x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(6x^2+11x=9x^2+5x \\ \Leftrightarrow -3x^2+6x=0 \\ \Leftrightarrow x(-3x+6) = 0 \\ \Leftrightarrow x = 0 \vee -3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-3} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
2. \(7x^2+22x=0 \\ \Leftrightarrow x(7x+22) = 0 \\ \Leftrightarrow x = 0 \vee 7x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{7} \\ V = \Big\{ 0 ; \frac{-22}{7} \Big\} \\ -----------------\)
3. \(-x^2-22x=0 \\ \Leftrightarrow x(-x-22) = 0 \\ \Leftrightarrow x = 0 \vee -x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-1} = -22 \\ V = \Big\{ 0 ; -22 \Big\} \\ -----------------\)
4. \(5x^2-10x=0 \\ \Leftrightarrow x(5x-10) = 0 \\ \Leftrightarrow x = 0 \vee 5x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{5} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
5. \(8x^2-10x=0 \\ \Leftrightarrow x(8x-10) = 0 \\ \Leftrightarrow x = 0 \vee 8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{8} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
6. \(-2x^2+17x=-8x^2-7x \\ \Leftrightarrow 6x^2+24x=0 \\ \Leftrightarrow x(6x+24) = 0 \\ \Leftrightarrow x = 0 \vee 6x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{6} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
7. \(-2(-10x^2+9x)=-(-18x^2+40x) \\ \Leftrightarrow 20x^2-18x=18x^2-40x \\ \Leftrightarrow 20x^2-18x-18x^2+40x= 0 \\ \Leftrightarrow 2x^2-22x=0 \\ \Leftrightarrow x(2x-22) = 0 \\ \Leftrightarrow x = 0 \vee 2x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{2} = 11 \\ V = \Big\{ 11; 0 \Big\} \\ -----------------\)
8. \(18x^2-3x=10x^2-8x \\ \Leftrightarrow 8x^2+5x=0 \\ \Leftrightarrow x(8x+5) = 0 \\ \Leftrightarrow x = 0 \vee 8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{8} \\ V = \Big\{ 0 ; \frac{-5}{8} \Big\} \\ -----------------\)
9. \(-3(5x^2+10x)=-(22x^2+24x) \\ \Leftrightarrow -15x^2-30x=-22x^2-24x \\ \Leftrightarrow -15x^2-30x+22x^2+24x= 0 \\ \Leftrightarrow 7x^2+6x=0 \\ \Leftrightarrow x(7x+6) = 0 \\ \Leftrightarrow x = 0 \vee 7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
10. \(5x^2+10x=-2x^2-8x \\ \Leftrightarrow 7x^2+18x=0 \\ \Leftrightarrow x(7x+18) = 0 \\ \Leftrightarrow x = 0 \vee 7x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{7} \\ V = \Big\{ 0 ; \frac{-18}{7} \Big\} \\ -----------------\)
11. \(-3(-9x^2+7x)=-(-20x^2+0x) \\ \Leftrightarrow 27x^2-21x=20x^2+0x \\ \Leftrightarrow 27x^2-21x-20x^2+0x= 0 \\ \Leftrightarrow 7x^2+21x=0 \\ \Leftrightarrow x(7x+21) = 0 \\ \Leftrightarrow x = 0 \vee 7x+21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-21}{7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(-6x^2-7x=0 \\ \Leftrightarrow x(-6x-7) = 0 \\ \Leftrightarrow x = 0 \vee -6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-6} = \frac{-7}{6} \\ V = \Big\{ 0 ; \frac{-7}{6} \Big\} \\ -----------------\)