Onvolledige VKV (c=0)

Hoofdmenu Eentje per keer  🖨

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+12x=5x^2-4x\)
2. \(-x^2-14x=0\)
3. \(-2(6x^2+5x)=-(13x^2+6x)\)
4. \(x^2-5x=0\)
5. \(-3(-10x^2-10x)=-(-26x^2-13x)\)
6. \(-7x^2+11x=0\)
7. \(x^2+20x=0\)
8. \(-12x^2+x=-7x^2-4x\)
9. \(-3(8x^2+2x)=-(22x^2+15x)\)
10. \(-5(-9x^2+2x)=-(-47x^2-x)\)
11. \(3(4x^2-5x)=-(-17x^2-x)\)
12. \(5(-7x^2-8x)=-(33x^2+23x)\)

---

Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+12x=5x^2-4x \\ \Leftrightarrow -8x^2+16x=0 \\ \Leftrightarrow x(-8x+16) = 0 \\ \Leftrightarrow x = 0 \vee -8x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-8} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
2. \(-x^2-14x=0 \\ \Leftrightarrow x(-x-14) = 0 \\ \Leftrightarrow x = 0 \vee -x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-1} = -14 \\ V = \Big\{ 0 ; -14 \Big\} \\ -----------------\)
3. \(-2(6x^2+5x)=-(13x^2+6x) \\ \Leftrightarrow -12x^2-10x=-13x^2-6x \\ \Leftrightarrow -12x^2-10x+13x^2+6x= 0 \\ \Leftrightarrow x^2+4x=0 \\ \Leftrightarrow x(x+4) = 0 \\ \Leftrightarrow x = 0 \vee x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{1} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)
4. \(x^2-5x=0 \\ \Leftrightarrow x(x-5) = 0 \\ \Leftrightarrow x = 0 \vee x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
5. \(-3(-10x^2-10x)=-(-26x^2-13x) \\ \Leftrightarrow 30x^2+30x=26x^2+13x \\ \Leftrightarrow 30x^2+30x-26x^2-13x= 0 \\ \Leftrightarrow 4x^2-17x=0 \\ \Leftrightarrow x(4x-17) = 0 \\ \Leftrightarrow x = 0 \vee 4x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{4} \\ V = \Big\{ \frac{17}{4}; 0 \Big\} \\ -----------------\)
6. \(-7x^2+11x=0 \\ \Leftrightarrow x(-7x+11) = 0 \\ \Leftrightarrow x = 0 \vee -7x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-7} = \frac{11}{7} \\ V = \Big\{ \frac{11}{7}; 0 \Big\} \\ -----------------\)
7. \(x^2+20x=0 \\ \Leftrightarrow x(x+20) = 0 \\ \Leftrightarrow x = 0 \vee x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{1} = -20 \\ V = \Big\{ 0 ; -20 \Big\} \\ -----------------\)
8. \(-12x^2+x=-7x^2-4x \\ \Leftrightarrow -5x^2+5x=0 \\ \Leftrightarrow x(-5x+5) = 0 \\ \Leftrightarrow x = 0 \vee -5x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
9. \(-3(8x^2+2x)=-(22x^2+15x) \\ \Leftrightarrow -24x^2-6x=-22x^2-15x \\ \Leftrightarrow -24x^2-6x+22x^2+15x= 0 \\ \Leftrightarrow -2x^2-9x=0 \\ \Leftrightarrow x(-2x-9) = 0 \\ \Leftrightarrow x = 0 \vee -2x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-2} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)
10. \(-5(-9x^2+2x)=-(-47x^2-x) \\ \Leftrightarrow 45x^2-10x=47x^2+x \\ \Leftrightarrow 45x^2-10x-47x^2-x= 0 \\ \Leftrightarrow -2x^2+11x=0 \\ \Leftrightarrow x(-2x+11) = 0 \\ \Leftrightarrow x = 0 \vee -2x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-2} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
11. \(3(4x^2-5x)=-(-17x^2-x) \\ \Leftrightarrow 12x^2-15x=17x^2+x \\ \Leftrightarrow 12x^2-15x-17x^2-x= 0 \\ \Leftrightarrow -5x^2+16x=0 \\ \Leftrightarrow x(-5x+16) = 0 \\ \Leftrightarrow x = 0 \vee -5x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-5} = \frac{16}{5} \\ V = \Big\{ \frac{16}{5}; 0 \Big\} \\ -----------------\)
12. \(5(-7x^2-8x)=-(33x^2+23x) \\ \Leftrightarrow -35x^2-40x=-33x^2-23x \\ \Leftrightarrow -35x^2-40x+33x^2+23x= 0 \\ \Leftrightarrow -2x^2+17x=0 \\ \Leftrightarrow x(-2x+17) = 0 \\ \Leftrightarrow x = 0 \vee -2x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-2} = \frac{17}{2} \\ V = \Big\{ \frac{17}{2}; 0 \Big\} \\ -----------------\)