Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(-10x^2-5x)=-(-36x^2+3x)\)
2. \(x^2+25x=5x^2+5x\)
3. \(7x^2-11x=0\)
4. \(-4x^2+9x=0\)
5. \(2x^2+1x=0\)
6. \(2(6x^2+4x)=-(-10x^2-24x)\)
7. \(6x^2+7x=8x^2+10x\)
8. \(3(3x^2-9x)=-(-2x^2+50x)\)
9. \(17x^2-6x=10x^2+3x\)
10. \(-4(-5x^2+3x)=-(-24x^2+10x)\)
11. \(-4(-7x^2-2x)=-(-25x^2+17x)\)
12. \(-3(9x^2+6x)=-(30x^2+38x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(-10x^2-5x)=-(-36x^2+3x) \\ \Leftrightarrow 30x^2+15x=36x^2-3x \\ \Leftrightarrow 30x^2+15x-36x^2+3x= 0 \\ \Leftrightarrow -6x^2-18x=0 \\ \Leftrightarrow x(-6x-18) = 0 \\ \Leftrightarrow x = 0 \vee -6x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(x^2+25x=5x^2+5x \\ \Leftrightarrow -4x^2+20x=0 \\ \Leftrightarrow x(-4x+20) = 0 \\ \Leftrightarrow x = 0 \vee -4x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
3. \(7x^2-11x=0 \\ \Leftrightarrow x(7x-11) = 0 \\ \Leftrightarrow x = 0 \vee 7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{7} \\ V = \Big\{ \frac{11}{7}; 0 \Big\} \\ -----------------\)
4. \(-4x^2+9x=0 \\ \Leftrightarrow x(-4x+9) = 0 \\ \Leftrightarrow x = 0 \vee -4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-4} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
5. \(2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
6. \(2(6x^2+4x)=-(-10x^2-24x) \\ \Leftrightarrow 12x^2+8x=10x^2+24x \\ \Leftrightarrow 12x^2+8x-10x^2-24x= 0 \\ \Leftrightarrow 2x^2+16x=0 \\ \Leftrightarrow x(2x+16) = 0 \\ \Leftrightarrow x = 0 \vee 2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
7. \(6x^2+7x=8x^2+10x \\ \Leftrightarrow -2x^2-3x=0 \\ \Leftrightarrow x(-2x-3) = 0 \\ \Leftrightarrow x = 0 \vee -2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-2} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
8. \(3(3x^2-9x)=-(-2x^2+50x) \\ \Leftrightarrow 9x^2-27x=2x^2-50x \\ \Leftrightarrow 9x^2-27x-2x^2+50x= 0 \\ \Leftrightarrow 7x^2-23x=0 \\ \Leftrightarrow x(7x-23) = 0 \\ \Leftrightarrow x = 0 \vee 7x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
9. \(17x^2-6x=10x^2+3x \\ \Leftrightarrow 7x^2-9x=0 \\ \Leftrightarrow x(7x-9) = 0 \\ \Leftrightarrow x = 0 \vee 7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
10. \(-4(-5x^2+3x)=-(-24x^2+10x) \\ \Leftrightarrow 20x^2-12x=24x^2-10x \\ \Leftrightarrow 20x^2-12x-24x^2+10x= 0 \\ \Leftrightarrow -4x^2+2x=0 \\ \Leftrightarrow x(-4x+2) = 0 \\ \Leftrightarrow x = 0 \vee -4x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-4} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)
11. \(-4(-7x^2-2x)=-(-25x^2+17x) \\ \Leftrightarrow 28x^2+8x=25x^2-17x \\ \Leftrightarrow 28x^2+8x-25x^2+17x= 0 \\ \Leftrightarrow 3x^2-25x=0 \\ \Leftrightarrow x(3x-25) = 0 \\ \Leftrightarrow x = 0 \vee 3x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{3} \\ V = \Big\{ \frac{25}{3}; 0 \Big\} \\ -----------------\)
12. \(-3(9x^2+6x)=-(30x^2+38x) \\ \Leftrightarrow -27x^2-18x=-30x^2-38x \\ \Leftrightarrow -27x^2-18x+30x^2+38x= 0 \\ \Leftrightarrow 3x^2-20x=0 \\ \Leftrightarrow x(3x-20) = 0 \\ \Leftrightarrow x = 0 \vee 3x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{3} \\ V = \Big\{ \frac{20}{3}; 0 \Big\} \\ -----------------\)