Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-8x^2-5x)=-(14x^2+25x)\)
2. \(-9x^2+9x=-4x^2-7x\)
3. \(5x^2+12x=8x^2+7x\)
4. \(-7x^2+22x=-9x^2-2x\)
5. \(-4x^2-30x=2x^2-7x\)
6. \(5(-3x^2+3x)=-(8x^2-7x)\)
7. \(-5(-9x^2+9x)=-(-43x^2+29x)\)
8. \(-6x^2+22x=0\)
9. \(6x^2+18x=8x^2-2x\)
10. \(-14x^2+29x=-9x^2+5x\)
11. \(6x^2+0x=0\)
12. \(-13x^2+14x=-10x^2+8x\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-8x^2-5x)=-(14x^2+25x) \\ \Leftrightarrow -16x^2-10x=-14x^2-25x \\ \Leftrightarrow -16x^2-10x+14x^2+25x= 0 \\ \Leftrightarrow -2x^2-15x=0 \\ \Leftrightarrow x(-2x-15) = 0 \\ \Leftrightarrow x = 0 \vee -2x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{-2} = \frac{-15}{2} \\ V = \Big\{ 0 ; \frac{-15}{2} \Big\} \\ -----------------\)
2. \(-9x^2+9x=-4x^2-7x \\ \Leftrightarrow -5x^2+16x=0 \\ \Leftrightarrow x(-5x+16) = 0 \\ \Leftrightarrow x = 0 \vee -5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-5} = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
3. \(5x^2+12x=8x^2+7x \\ \Leftrightarrow -3x^2+5x=0 \\ \Leftrightarrow x(-3x+5) = 0 \\ \Leftrightarrow x = 0 \vee -3x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-3} = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)
4. \(-7x^2+22x=-9x^2-2x \\ \Leftrightarrow 2x^2+24x=0 \\ \Leftrightarrow x(2x+24) = 0 \\ \Leftrightarrow x = 0 \vee 2x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{2} = -12 \\ V = \Big\{ 0 ; -12 \Big\} \\ -----------------\)
5. \(-4x^2-30x=2x^2-7x \\ \Leftrightarrow -6x^2-23x=0 \\ \Leftrightarrow x(-6x-23) = 0 \\ \Leftrightarrow x = 0 \vee -6x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-6} = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
6. \(5(-3x^2+3x)=-(8x^2-7x) \\ \Leftrightarrow -15x^2+15x=-8x^2+7x \\ \Leftrightarrow -15x^2+15x+8x^2-7x= 0 \\ \Leftrightarrow -7x^2-8x=0 \\ \Leftrightarrow x(-7x-8) = 0 \\ \Leftrightarrow x = 0 \vee -7x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-7} = \frac{-8}{7} \\ V = \Big\{ 0 ; \frac{-8}{7} \Big\} \\ -----------------\)
7. \(-5(-9x^2+9x)=-(-43x^2+29x) \\ \Leftrightarrow 45x^2-45x=43x^2-29x \\ \Leftrightarrow 45x^2-45x-43x^2+29x= 0 \\ \Leftrightarrow 2x^2+16x=0 \\ \Leftrightarrow x(2x+16) = 0 \\ \Leftrightarrow x = 0 \vee 2x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{2} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
8. \(-6x^2+22x=0 \\ \Leftrightarrow x(-6x+22) = 0 \\ \Leftrightarrow x = 0 \vee -6x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
9. \(6x^2+18x=8x^2-2x \\ \Leftrightarrow -2x^2+20x=0 \\ \Leftrightarrow x(-2x+20) = 0 \\ \Leftrightarrow x = 0 \vee -2x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-2} = 10 \\ V = \Big\{ 10; 0 \Big\} \\ -----------------\)
10. \(-14x^2+29x=-9x^2+5x \\ \Leftrightarrow -5x^2+24x=0 \\ \Leftrightarrow x(-5x+24) = 0 \\ \Leftrightarrow x = 0 \vee -5x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-5} = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
11. \(6x^2+0x=0 \\ \Leftrightarrow 6x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{6} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-13x^2+14x=-10x^2+8x \\ \Leftrightarrow -3x^2+6x=0 \\ \Leftrightarrow x(-3x+6) = 0 \\ \Leftrightarrow x = 0 \vee -3x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-3} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)