Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-10x^2+7x)=-(-16x^2+2x)\)
2. \(3x^2+9x=0\)
3. \(-6x^2-24x=0\)
4. \(-x^2+27x=7x^2+4x\)
5. \(3(10x^2-10x)=-(-33x^2+35x)\)
6. \(2(10x^2+7x)=-(-18x^2-27x)\)
7. \(-5x^2-20x=0\)
8. \(4(-7x^2+2x)=-(29x^2-23x)\)
9. \(7x^2-10x=0\)
10. \(3(8x^2-6x)=-(-19x^2+11x)\)
11. \(-4(-7x^2-10x)=-(-29x^2-63x)\)
12. \(-3(8x^2-3x)=-(31x^2-9x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-10x^2+7x)=-(-16x^2+2x) \\ \Leftrightarrow 20x^2-14x=16x^2-2x \\ \Leftrightarrow 20x^2-14x-16x^2+2x= 0 \\ \Leftrightarrow 4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(3x^2+9x=0 \\ \Leftrightarrow x(3x+9) = 0 \\ \Leftrightarrow x = 0 \vee 3x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{3} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
3. \(-6x^2-24x=0 \\ \Leftrightarrow x(-6x-24) = 0 \\ \Leftrightarrow x = 0 \vee -6x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-6} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
4. \(-x^2+27x=7x^2+4x \\ \Leftrightarrow -8x^2+23x=0 \\ \Leftrightarrow x(-8x+23) = 0 \\ \Leftrightarrow x = 0 \vee -8x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-8} = \frac{23}{8} \\ V = \Big\{ \frac{23}{8}; 0 \Big\} \\ -----------------\)
5. \(3(10x^2-10x)=-(-33x^2+35x) \\ \Leftrightarrow 30x^2-30x=33x^2-35x \\ \Leftrightarrow 30x^2-30x-33x^2+35x= 0 \\ \Leftrightarrow -3x^2-5x=0 \\ \Leftrightarrow x(-3x-5) = 0 \\ \Leftrightarrow x = 0 \vee -3x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-3} = \frac{-5}{3} \\ V = \Big\{ 0 ; \frac{-5}{3} \Big\} \\ -----------------\)
6. \(2(10x^2+7x)=-(-18x^2-27x) \\ \Leftrightarrow 20x^2+14x=18x^2+27x \\ \Leftrightarrow 20x^2+14x-18x^2-27x= 0 \\ \Leftrightarrow 2x^2+13x=0 \\ \Leftrightarrow x(2x+13) = 0 \\ \Leftrightarrow x = 0 \vee 2x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{2} \\ V = \Big\{ 0 ; \frac{-13}{2} \Big\} \\ -----------------\)
7. \(-5x^2-20x=0 \\ \Leftrightarrow x(-5x-20) = 0 \\ \Leftrightarrow x = 0 \vee -5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-5} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
8. \(4(-7x^2+2x)=-(29x^2-23x) \\ \Leftrightarrow -28x^2+8x=-29x^2+23x \\ \Leftrightarrow -28x^2+8x+29x^2-23x= 0 \\ \Leftrightarrow x^2+15x=0 \\ \Leftrightarrow x(x+15) = 0 \\ \Leftrightarrow x = 0 \vee x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{1} = -15 \\ V = \Big\{ 0 ; -15 \Big\} \\ -----------------\)
9. \(7x^2-10x=0 \\ \Leftrightarrow x(7x-10) = 0 \\ \Leftrightarrow x = 0 \vee 7x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{7} \\ V = \Big\{ \frac{10}{7}; 0 \Big\} \\ -----------------\)
10. \(3(8x^2-6x)=-(-19x^2+11x) \\ \Leftrightarrow 24x^2-18x=19x^2-11x \\ \Leftrightarrow 24x^2-18x-19x^2+11x= 0 \\ \Leftrightarrow 5x^2+7x=0 \\ \Leftrightarrow x(5x+7) = 0 \\ \Leftrightarrow x = 0 \vee 5x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{5} \\ V = \Big\{ 0 ; \frac{-7}{5} \Big\} \\ -----------------\)
11. \(-4(-7x^2-10x)=-(-29x^2-63x) \\ \Leftrightarrow 28x^2+40x=29x^2+63x \\ \Leftrightarrow 28x^2+40x-29x^2-63x= 0 \\ \Leftrightarrow -x^2+23x=0 \\ \Leftrightarrow x(-x+23) = 0 \\ \Leftrightarrow x = 0 \vee -x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
12. \(-3(8x^2-3x)=-(31x^2-9x) \\ \Leftrightarrow -24x^2+9x=-31x^2+9x \\ \Leftrightarrow -24x^2+9x+31x^2-9x= 0 \\ \Leftrightarrow 7x^2+0x=0 \\ \Leftrightarrow 7x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{7} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)