Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(9x^2-7x)=-(-12x^2+36x)\)
2. \(-11x^2-6x=-10x^2+10x\)
3. \(-2x^2-16x=0\)
4. \(-10x^2+4x=-6x^2-3x\)
5. \(-5x^2+17x=0\)
6. \(7x^2+26x=6x^2+2x\)
7. \(-4(5x^2+6x)=-(18x^2+12x)\)
8. \(-7x^2-3x=-2x^2+7x\)
9. \(4(-3x^2+3x)=-(13x^2-2x)\)
10. \(-8x^2-7x=0\)
11. \(-4x^2-2x=-9x^2-4x\)
12. \(2x^2-24x=0\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(9x^2-7x)=-(-12x^2+36x) \\ \Leftrightarrow 18x^2-14x=12x^2-36x \\ \Leftrightarrow 18x^2-14x-12x^2+36x= 0 \\ \Leftrightarrow 6x^2-22x=0 \\ \Leftrightarrow x(6x-22) = 0 \\ \Leftrightarrow x = 0 \vee 6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
2. \(-11x^2-6x=-10x^2+10x \\ \Leftrightarrow -x^2-16x=0 \\ \Leftrightarrow x(-x-16) = 0 \\ \Leftrightarrow x = 0 \vee -x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-1} = -16 \\ V = \Big\{ 0 ; -16 \Big\} \\ -----------------\)
3. \(-2x^2-16x=0 \\ \Leftrightarrow x(-2x-16) = 0 \\ \Leftrightarrow x = 0 \vee -2x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
4. \(-10x^2+4x=-6x^2-3x \\ \Leftrightarrow -4x^2+7x=0 \\ \Leftrightarrow x(-4x+7) = 0 \\ \Leftrightarrow x = 0 \vee -4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-4} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
5. \(-5x^2+17x=0 \\ \Leftrightarrow x(-5x+17) = 0 \\ \Leftrightarrow x = 0 \vee -5x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-5} = \frac{17}{5} \\ V = \Big\{ \frac{17}{5}; 0 \Big\} \\ -----------------\)
6. \(7x^2+26x=6x^2+2x \\ \Leftrightarrow x^2+24x=0 \\ \Leftrightarrow x(x+24) = 0 \\ \Leftrightarrow x = 0 \vee x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
7. \(-4(5x^2+6x)=-(18x^2+12x) \\ \Leftrightarrow -20x^2-24x=-18x^2-12x \\ \Leftrightarrow -20x^2-24x+18x^2+12x= 0 \\ \Leftrightarrow -2x^2+12x=0 \\ \Leftrightarrow x(-2x+12) = 0 \\ \Leftrightarrow x = 0 \vee -2x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{-2} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
8. \(-7x^2-3x=-2x^2+7x \\ \Leftrightarrow -5x^2-10x=0 \\ \Leftrightarrow x(-5x-10) = 0 \\ \Leftrightarrow x = 0 \vee -5x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-5} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
9. \(4(-3x^2+3x)=-(13x^2-2x) \\ \Leftrightarrow -12x^2+12x=-13x^2+2x \\ \Leftrightarrow -12x^2+12x+13x^2-2x= 0 \\ \Leftrightarrow x^2-10x=0 \\ \Leftrightarrow x(x-10) = 0 \\ \Leftrightarrow x = 0 \vee x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{1} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
10. \(-8x^2-7x=0 \\ \Leftrightarrow x(-8x-7) = 0 \\ \Leftrightarrow x = 0 \vee -8x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{-8} = \frac{-7}{8} \\ V = \Big\{ 0 ; \frac{-7}{8} \Big\} \\ -----------------\)
11. \(-4x^2-2x=-9x^2-4x \\ \Leftrightarrow 5x^2+2x=0 \\ \Leftrightarrow x(5x+2) = 0 \\ \Leftrightarrow x = 0 \vee 5x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{5} \\ V = \Big\{ 0 ; \frac{-2}{5} \Big\} \\ -----------------\)
12. \(2x^2-24x=0 \\ \Leftrightarrow x(2x-24) = 0 \\ \Leftrightarrow x = 0 \vee 2x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{2} = 12 \\ V = \Big\{ 12; 0 \Big\} \\ -----------------\)