Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2-18x=-5x^2+5x\)
2. \(-6x^2+13x=-4x^2-10x\)
3. \(-2x^2-4x=-4x^2-4x\)
4. \(-5x^2-19x=0\)
5. \(-7x^2+25x=0\)
6. \(-5x^2-x=-4x^2+2x\)
7. \(2x^2-8x=0\)
8. \(-2x^2-20x=-9x^2+2x\)
9. \(5(4x^2+7x)=-(-28x^2-38x)\)
10. \(-12x^2-7x=-10x^2+2x\)
11. \(-14x^2-17x=-6x^2-2x\)
12. \(-4(-4x^2-10x)=-(-10x^2-34x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2-18x=-5x^2+5x \\ \Leftrightarrow 4x^2-23x=0 \\ \Leftrightarrow x(4x-23) = 0 \\ \Leftrightarrow x = 0 \vee 4x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{4} \\ V = \Big\{ \frac{23}{4}; 0 \Big\} \\ -----------------\)
2. \(-6x^2+13x=-4x^2-10x \\ \Leftrightarrow -2x^2+23x=0 \\ \Leftrightarrow x(-2x+23) = 0 \\ \Leftrightarrow x = 0 \vee -2x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-2} = \frac{23}{2} \\ V = \Big\{ \frac{23}{2}; 0 \Big\} \\ -----------------\)
3. \(-2x^2-4x=-4x^2-4x \\ \Leftrightarrow 2x^2+0x=0 \\ \Leftrightarrow 2x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{2} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-5x^2-19x=0 \\ \Leftrightarrow x(-5x-19) = 0 \\ \Leftrightarrow x = 0 \vee -5x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-5} = \frac{-19}{5} \\ V = \Big\{ 0 ; \frac{-19}{5} \Big\} \\ -----------------\)
5. \(-7x^2+25x=0 \\ \Leftrightarrow x(-7x+25) = 0 \\ \Leftrightarrow x = 0 \vee -7x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-7} = \frac{25}{7} \\ V = \Big\{ \frac{25}{7}; 0 \Big\} \\ -----------------\)
6. \(-5x^2-x=-4x^2+2x \\ \Leftrightarrow -x^2-3x=0 \\ \Leftrightarrow x(-x-3) = 0 \\ \Leftrightarrow x = 0 \vee -x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-1} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
7. \(2x^2-8x=0 \\ \Leftrightarrow x(2x-8) = 0 \\ \Leftrightarrow x = 0 \vee 2x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{2} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
8. \(-2x^2-20x=-9x^2+2x \\ \Leftrightarrow 7x^2-22x=0 \\ \Leftrightarrow x(7x-22) = 0 \\ \Leftrightarrow x = 0 \vee 7x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{7} \\ V = \Big\{ \frac{22}{7}; 0 \Big\} \\ -----------------\)
9. \(5(4x^2+7x)=-(-28x^2-38x) \\ \Leftrightarrow 20x^2+35x=28x^2+38x \\ \Leftrightarrow 20x^2+35x-28x^2-38x= 0 \\ \Leftrightarrow -8x^2+3x=0 \\ \Leftrightarrow x(-8x+3) = 0 \\ \Leftrightarrow x = 0 \vee -8x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-8} = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)
10. \(-12x^2-7x=-10x^2+2x \\ \Leftrightarrow -2x^2-9x=0 \\ \Leftrightarrow x(-2x-9) = 0 \\ \Leftrightarrow x = 0 \vee -2x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-2} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
11. \(-14x^2-17x=-6x^2-2x \\ \Leftrightarrow -8x^2-15x=0 \\ \Leftrightarrow x(-8x-15) = 0 \\ \Leftrightarrow x = 0 \vee -8x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-8} = \frac{-15}{8} \\ V = \Big\{ 0 ; \frac{-15}{8} \Big\} \\ -----------------\)
12. \(-4(-4x^2-10x)=-(-10x^2-34x) \\ \Leftrightarrow 16x^2+40x=10x^2+34x \\ \Leftrightarrow 16x^2+40x-10x^2-34x= 0 \\ \Leftrightarrow 6x^2-6x=0 \\ \Leftrightarrow x(6x-6) = 0 \\ \Leftrightarrow x = 0 \vee 6x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)