Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-7x^2-24x=0\)
2. \(-7x^2-10x=0\)
3. \(3x^2+2x=0\)
4. \(-5x^2-13x=0\)
5. \(4x^2-4x=-3x^2-3x\)
6. \(-4(-8x^2-5x)=-(-25x^2-18x)\)
7. \(5(8x^2-6x)=-(-37x^2+22x)\)
8. \(6x^2-14x=-2x^2+8x\)
9. \(-11x^2-25x=-3x^2-3x\)
10. \(4(4x^2+5x)=-(-13x^2-36x)\)
11. \(-x^2-21x=2x^2-8x\)
12. \(-4(9x^2-6x)=-(30x^2-34x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-7x^2-24x=0 \\ \Leftrightarrow x(-7x-24) = 0 \\ \Leftrightarrow x = 0 \vee -7x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-7} = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
2. \(-7x^2-10x=0 \\ \Leftrightarrow x(-7x-10) = 0 \\ \Leftrightarrow x = 0 \vee -7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-7} = \frac{-10}{7} \\ V = \Big\{ 0 ; \frac{-10}{7} \Big\} \\ -----------------\)
3. \(3x^2+2x=0 \\ \Leftrightarrow x(3x+2) = 0 \\ \Leftrightarrow x = 0 \vee 3x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{3} \\ V = \Big\{ 0 ; \frac{-2}{3} \Big\} \\ -----------------\)
4. \(-5x^2-13x=0 \\ \Leftrightarrow x(-5x-13) = 0 \\ \Leftrightarrow x = 0 \vee -5x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-5} = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
5. \(4x^2-4x=-3x^2-3x \\ \Leftrightarrow 7x^2-1x=0 \\ \Leftrightarrow x(7x-1) = 0 \\ \Leftrightarrow x = 0 \vee 7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{7} \\ V = \Big\{ \frac{1}{7}; 0 \Big\} \\ -----------------\)
6. \(-4(-8x^2-5x)=-(-25x^2-18x) \\ \Leftrightarrow 32x^2+20x=25x^2+18x \\ \Leftrightarrow 32x^2+20x-25x^2-18x= 0 \\ \Leftrightarrow 7x^2-2x=0 \\ \Leftrightarrow x(7x-2) = 0 \\ \Leftrightarrow x = 0 \vee 7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)
7. \(5(8x^2-6x)=-(-37x^2+22x) \\ \Leftrightarrow 40x^2-30x=37x^2-22x \\ \Leftrightarrow 40x^2-30x-37x^2+22x= 0 \\ \Leftrightarrow 3x^2+8x=0 \\ \Leftrightarrow x(3x+8) = 0 \\ \Leftrightarrow x = 0 \vee 3x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{3} \\ V = \Big\{ 0 ; \frac{-8}{3} \Big\} \\ -----------------\)
8. \(6x^2-14x=-2x^2+8x \\ \Leftrightarrow 8x^2-22x=0 \\ \Leftrightarrow x(8x-22) = 0 \\ \Leftrightarrow x = 0 \vee 8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{8} = \frac{11}{4} \\ V = \Big\{ \frac{11}{4}; 0 \Big\} \\ -----------------\)
9. \(-11x^2-25x=-3x^2-3x \\ \Leftrightarrow -8x^2-22x=0 \\ \Leftrightarrow x(-8x-22) = 0 \\ \Leftrightarrow x = 0 \vee -8x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-8} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
10. \(4(4x^2+5x)=-(-13x^2-36x) \\ \Leftrightarrow 16x^2+20x=13x^2+36x \\ \Leftrightarrow 16x^2+20x-13x^2-36x= 0 \\ \Leftrightarrow 3x^2+16x=0 \\ \Leftrightarrow x(3x+16) = 0 \\ \Leftrightarrow x = 0 \vee 3x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
11. \(-x^2-21x=2x^2-8x \\ \Leftrightarrow -3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
12. \(-4(9x^2-6x)=-(30x^2-34x) \\ \Leftrightarrow -36x^2+24x=-30x^2+34x \\ \Leftrightarrow -36x^2+24x+30x^2-34x= 0 \\ \Leftrightarrow -6x^2+10x=0 \\ \Leftrightarrow x(-6x+10) = 0 \\ \Leftrightarrow x = 0 \vee -6x+10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-10}{-6} = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)