Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-7x^2-3x)=-(10x^2+0x)\)
2. \(4x^2+12x=0\)
3. \(-2x^2-7x=-9x^2-4x\)
4. \(5(8x^2+7x)=-(-37x^2-38x)\)
5. \(-x^2+7x=0\)
6. \(-5(-8x^2+4x)=-(-39x^2+18x)\)
7. \(x^2-3x=4x^2+10x\)
8. \(-3x^2-16x=0\)
9. \(14x^2-16x=8x^2-7x\)
10. \(3(8x^2-6x)=-(-18x^2+19x)\)
11. \(4(10x^2-3x)=-(-39x^2-13x)\)
12. \(-5(7x^2-4x)=-(34x^2+2x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-7x^2-3x)=-(10x^2+0x) \\ \Leftrightarrow -14x^2-6x=-10x^2+0x \\ \Leftrightarrow -14x^2-6x+10x^2+0x= 0 \\ \Leftrightarrow -4x^2+6x=0 \\ \Leftrightarrow x(-4x+6) = 0 \\ \Leftrightarrow x = 0 \vee -4x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-4} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
2. \(4x^2+12x=0 \\ \Leftrightarrow x(4x+12) = 0 \\ \Leftrightarrow x = 0 \vee 4x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{4} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
3. \(-2x^2-7x=-9x^2-4x \\ \Leftrightarrow 7x^2-3x=0 \\ \Leftrightarrow x(7x-3) = 0 \\ \Leftrightarrow x = 0 \vee 7x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{7} \\ V = \Big\{ \frac{3}{7}; 0 \Big\} \\ -----------------\)
4. \(5(8x^2+7x)=-(-37x^2-38x) \\ \Leftrightarrow 40x^2+35x=37x^2+38x \\ \Leftrightarrow 40x^2+35x-37x^2-38x= 0 \\ \Leftrightarrow 3x^2+3x=0 \\ \Leftrightarrow x(3x+3) = 0 \\ \Leftrightarrow x = 0 \vee 3x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{3} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
5. \(-x^2+7x=0 \\ \Leftrightarrow x(-x+7) = 0 \\ \Leftrightarrow x = 0 \vee -x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
6. \(-5(-8x^2+4x)=-(-39x^2+18x) \\ \Leftrightarrow 40x^2-20x=39x^2-18x \\ \Leftrightarrow 40x^2-20x-39x^2+18x= 0 \\ \Leftrightarrow x^2+2x=0 \\ \Leftrightarrow x(x+2) = 0 \\ \Leftrightarrow x = 0 \vee x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{1} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
7. \(x^2-3x=4x^2+10x \\ \Leftrightarrow -3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
8. \(-3x^2-16x=0 \\ \Leftrightarrow x(-3x-16) = 0 \\ \Leftrightarrow x = 0 \vee -3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-3} = \frac{-16}{3} \\ V = \Big\{ 0 ; \frac{-16}{3} \Big\} \\ -----------------\)
9. \(14x^2-16x=8x^2-7x \\ \Leftrightarrow 6x^2-9x=0 \\ \Leftrightarrow x(6x-9) = 0 \\ \Leftrightarrow x = 0 \vee 6x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{6} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
10. \(3(8x^2-6x)=-(-18x^2+19x) \\ \Leftrightarrow 24x^2-18x=18x^2-19x \\ \Leftrightarrow 24x^2-18x-18x^2+19x= 0 \\ \Leftrightarrow 6x^2-1x=0 \\ \Leftrightarrow x(6x-1) = 0 \\ \Leftrightarrow x = 0 \vee 6x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{6} \\ V = \Big\{ \frac{1}{6}; 0 \Big\} \\ -----------------\)
11. \(4(10x^2-3x)=-(-39x^2-13x) \\ \Leftrightarrow 40x^2-12x=39x^2+13x \\ \Leftrightarrow 40x^2-12x-39x^2-13x= 0 \\ \Leftrightarrow x^2+25x=0 \\ \Leftrightarrow x(x+25) = 0 \\ \Leftrightarrow x = 0 \vee x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{1} = -25 \\ V = \Big\{ 0 ; -25 \Big\} \\ -----------------\)
12. \(-5(7x^2-4x)=-(34x^2+2x) \\ \Leftrightarrow -35x^2+20x=-34x^2-2x \\ \Leftrightarrow -35x^2+20x+34x^2+2x= 0 \\ \Leftrightarrow -x^2-22x=0 \\ \Leftrightarrow x(-x-22) = 0 \\ \Leftrightarrow x = 0 \vee -x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-1} = -22 \\ V = \Big\{ 0 ; -22 \Big\} \\ -----------------\)