Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+9x=0\)
2. \(4x^2-19x=0\)
3. \(-17x^2-2x=-10x^2-6x\)
4. \(-5x^2+8x=0\)
5. \(-8x^2+3x=0\)
6. \(-x^2+24x=-5x^2+4x\)
7. \(-8x^2+17x=0\)
8. \(-5(9x^2+9x)=-(46x^2+66x)\)
9. \(-4x^2+19x=-5x^2+5x\)
10. \(-3(10x^2-5x)=-(27x^2-2x)\)
11. \(-2x^2+11x=0\)
12. \(6x^2+11x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+9x=0 \\ \Leftrightarrow x(-4x+9) = 0 \\ \Leftrightarrow x = 0 \vee -4x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-4} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
2. \(4x^2-19x=0 \\ \Leftrightarrow x(4x-19) = 0 \\ \Leftrightarrow x = 0 \vee 4x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{4} \\ V = \Big\{ \frac{19}{4}; 0 \Big\} \\ -----------------\)
3. \(-17x^2-2x=-10x^2-6x \\ \Leftrightarrow -7x^2+4x=0 \\ \Leftrightarrow x(-7x+4) = 0 \\ \Leftrightarrow x = 0 \vee -7x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-7} = \frac{4}{7} \\ V = \Big\{ \frac{4}{7}; 0 \Big\} \\ -----------------\)
4. \(-5x^2+8x=0 \\ \Leftrightarrow x(-5x+8) = 0 \\ \Leftrightarrow x = 0 \vee -5x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-5} = \frac{8}{5} \\ V = \Big\{ \frac{8}{5}; 0 \Big\} \\ -----------------\)
5. \(-8x^2+3x=0 \\ \Leftrightarrow x(-8x+3) = 0 \\ \Leftrightarrow x = 0 \vee -8x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-8} = \frac{3}{8} \\ V = \Big\{ \frac{3}{8}; 0 \Big\} \\ -----------------\)
6. \(-x^2+24x=-5x^2+4x \\ \Leftrightarrow 4x^2+20x=0 \\ \Leftrightarrow x(4x+20) = 0 \\ \Leftrightarrow x = 0 \vee 4x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{4} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)
7. \(-8x^2+17x=0 \\ \Leftrightarrow x(-8x+17) = 0 \\ \Leftrightarrow x = 0 \vee -8x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{-8} = \frac{17}{8} \\ V = \Big\{ \frac{17}{8}; 0 \Big\} \\ -----------------\)
8. \(-5(9x^2+9x)=-(46x^2+66x) \\ \Leftrightarrow -45x^2-45x=-46x^2-66x \\ \Leftrightarrow -45x^2-45x+46x^2+66x= 0 \\ \Leftrightarrow x^2-21x=0 \\ \Leftrightarrow x(x-21) = 0 \\ \Leftrightarrow x = 0 \vee x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{1} = 21 \\ V = \Big\{ 21; 0 \Big\} \\ -----------------\)
9. \(-4x^2+19x=-5x^2+5x \\ \Leftrightarrow x^2+14x=0 \\ \Leftrightarrow x(x+14) = 0 \\ \Leftrightarrow x = 0 \vee x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{1} = -14 \\ V = \Big\{ 0 ; -14 \Big\} \\ -----------------\)
10. \(-3(10x^2-5x)=-(27x^2-2x) \\ \Leftrightarrow -30x^2+15x=-27x^2+2x \\ \Leftrightarrow -30x^2+15x+27x^2-2x= 0 \\ \Leftrightarrow -3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
11. \(-2x^2+11x=0 \\ \Leftrightarrow x(-2x+11) = 0 \\ \Leftrightarrow x = 0 \vee -2x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-2} = \frac{11}{2} \\ V = \Big\{ \frac{11}{2}; 0 \Big\} \\ -----------------\)
12. \(6x^2+11x=0 \\ \Leftrightarrow x(6x+11) = 0 \\ \Leftrightarrow x = 0 \vee 6x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{6} \\ V = \Big\{ 0 ; \frac{-11}{6} \Big\} \\ -----------------\)