Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2+11x=10x^2+2x\)
2. \(-x^2-31x=-7x^2-6x\)
3. \(6x^2+13x=0\)
4. \(-8x^2+11x=0\)
5. \(-5(2x^2-8x)=-(4x^2-44x)\)
6. \(4(8x^2-8x)=-(-25x^2+19x)\)
7. \(4x^2-7x=-4x^2+7x\)
8. \(-8x^2-24x=0\)
9. \(7x^2-6x=0\)
10. \(3(-7x^2+10x)=-(27x^2-47x)\)
11. \(-8x^2+5x=0\)
12. \(3x^2-4x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2+11x=10x^2+2x \\ \Leftrightarrow -8x^2+9x=0 \\ \Leftrightarrow x(-8x+9) = 0 \\ \Leftrightarrow x = 0 \vee -8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-8} = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
2. \(-x^2-31x=-7x^2-6x \\ \Leftrightarrow 6x^2-25x=0 \\ \Leftrightarrow x(6x-25) = 0 \\ \Leftrightarrow x = 0 \vee 6x-25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{25}{6} \\ V = \Big\{ \frac{25}{6}; 0 \Big\} \\ -----------------\)
3. \(6x^2+13x=0 \\ \Leftrightarrow x(6x+13) = 0 \\ \Leftrightarrow x = 0 \vee 6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
4. \(-8x^2+11x=0 \\ \Leftrightarrow x(-8x+11) = 0 \\ \Leftrightarrow x = 0 \vee -8x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-8} = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
5. \(-5(2x^2-8x)=-(4x^2-44x) \\ \Leftrightarrow -10x^2+40x=-4x^2+44x \\ \Leftrightarrow -10x^2+40x+4x^2-44x= 0 \\ \Leftrightarrow -6x^2+4x=0 \\ \Leftrightarrow x(-6x+4) = 0 \\ \Leftrightarrow x = 0 \vee -6x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
6. \(4(8x^2-8x)=-(-25x^2+19x) \\ \Leftrightarrow 32x^2-32x=25x^2-19x \\ \Leftrightarrow 32x^2-32x-25x^2+19x= 0 \\ \Leftrightarrow 7x^2+13x=0 \\ \Leftrightarrow x(7x+13) = 0 \\ \Leftrightarrow x = 0 \vee 7x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{7} \\ V = \Big\{ 0 ; \frac{-13}{7} \Big\} \\ -----------------\)
7. \(4x^2-7x=-4x^2+7x \\ \Leftrightarrow 8x^2-14x=0 \\ \Leftrightarrow x(8x-14) = 0 \\ \Leftrightarrow x = 0 \vee 8x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{8} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
8. \(-8x^2-24x=0 \\ \Leftrightarrow x(-8x-24) = 0 \\ \Leftrightarrow x = 0 \vee -8x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-8} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
9. \(7x^2-6x=0 \\ \Leftrightarrow x(7x-6) = 0 \\ \Leftrightarrow x = 0 \vee 7x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{7} \\ V = \Big\{ \frac{6}{7}; 0 \Big\} \\ -----------------\)
10. \(3(-7x^2+10x)=-(27x^2-47x) \\ \Leftrightarrow -21x^2+30x=-27x^2+47x \\ \Leftrightarrow -21x^2+30x+27x^2-47x= 0 \\ \Leftrightarrow 6x^2+17x=0 \\ \Leftrightarrow x(6x+17) = 0 \\ \Leftrightarrow x = 0 \vee 6x+17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-17}{6} \\ V = \Big\{ 0 ; \frac{-17}{6} \Big\} \\ -----------------\)
11. \(-8x^2+5x=0 \\ \Leftrightarrow x(-8x+5) = 0 \\ \Leftrightarrow x = 0 \vee -8x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-8} = \frac{5}{8} \\ V = \Big\{ \frac{5}{8}; 0 \Big\} \\ -----------------\)
12. \(3x^2-4x=0 \\ \Leftrightarrow x(3x-4) = 0 \\ \Leftrightarrow x = 0 \vee 3x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{3} \\ V = \Big\{ \frac{4}{3}; 0 \Big\} \\ -----------------\)