Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(10x^2-8x)=-(-27x^2+33x)\)
2. \(10x^2-6x=3x^2+3x\)
3. \(2x^2-4x=0\)
4. \(5(10x^2+3x)=-(-46x^2-28x)\)
5. \(5x^2+14x=0\)
6. \(13x^2-20x=10x^2-4x\)
7. \(2(-4x^2+7x)=-(9x^2+0x)\)
8. \(-3(-10x^2+9x)=-(-25x^2+45x)\)
9. \(-3x^2+9x=5x^2-6x\)
10. \(4x^2-10x=10x^2+3x\)
11. \(8x^2+12x=0\)
12. \(-4x^2-16x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(10x^2-8x)=-(-27x^2+33x) \\ \Leftrightarrow 20x^2-16x=27x^2-33x \\ \Leftrightarrow 20x^2-16x-27x^2+33x= 0 \\ \Leftrightarrow -7x^2-17x=0 \\ \Leftrightarrow x(-7x-17) = 0 \\ \Leftrightarrow x = 0 \vee -7x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-7} = \frac{-17}{7} \\ V = \Big\{ 0 ; \frac{-17}{7} \Big\} \\ -----------------\)
2. \(10x^2-6x=3x^2+3x \\ \Leftrightarrow 7x^2-9x=0 \\ \Leftrightarrow x(7x-9) = 0 \\ \Leftrightarrow x = 0 \vee 7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)
3. \(2x^2-4x=0 \\ \Leftrightarrow x(2x-4) = 0 \\ \Leftrightarrow x = 0 \vee 2x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{2} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
4. \(5(10x^2+3x)=-(-46x^2-28x) \\ \Leftrightarrow 50x^2+15x=46x^2+28x \\ \Leftrightarrow 50x^2+15x-46x^2-28x= 0 \\ \Leftrightarrow 4x^2+13x=0 \\ \Leftrightarrow x(4x+13) = 0 \\ \Leftrightarrow x = 0 \vee 4x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{4} \\ V = \Big\{ 0 ; \frac{-13}{4} \Big\} \\ -----------------\)
5. \(5x^2+14x=0 \\ \Leftrightarrow x(5x+14) = 0 \\ \Leftrightarrow x = 0 \vee 5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
6. \(13x^2-20x=10x^2-4x \\ \Leftrightarrow 3x^2-16x=0 \\ \Leftrightarrow x(3x-16) = 0 \\ \Leftrightarrow x = 0 \vee 3x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{3} \\ V = \Big\{ \frac{16}{3}; 0 \Big\} \\ -----------------\)
7. \(2(-4x^2+7x)=-(9x^2+0x) \\ \Leftrightarrow -8x^2+14x=-9x^2+0x \\ \Leftrightarrow -8x^2+14x+9x^2+0x= 0 \\ \Leftrightarrow x^2-14x=0 \\ \Leftrightarrow x(x-14) = 0 \\ \Leftrightarrow x = 0 \vee x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{1} = 14 \\ V = \Big\{ 14; 0 \Big\} \\ -----------------\)
8. \(-3(-10x^2+9x)=-(-25x^2+45x) \\ \Leftrightarrow 30x^2-27x=25x^2-45x \\ \Leftrightarrow 30x^2-27x-25x^2+45x= 0 \\ \Leftrightarrow 5x^2-18x=0 \\ \Leftrightarrow x(5x-18) = 0 \\ \Leftrightarrow x = 0 \vee 5x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{5} \\ V = \Big\{ \frac{18}{5}; 0 \Big\} \\ -----------------\)
9. \(-3x^2+9x=5x^2-6x \\ \Leftrightarrow -8x^2+15x=0 \\ \Leftrightarrow x(-8x+15) = 0 \\ \Leftrightarrow x = 0 \vee -8x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-8} = \frac{15}{8} \\ V = \Big\{ \frac{15}{8}; 0 \Big\} \\ -----------------\)
10. \(4x^2-10x=10x^2+3x \\ \Leftrightarrow -6x^2-13x=0 \\ \Leftrightarrow x(-6x-13) = 0 \\ \Leftrightarrow x = 0 \vee -6x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-6} = \frac{-13}{6} \\ V = \Big\{ 0 ; \frac{-13}{6} \Big\} \\ -----------------\)
11. \(8x^2+12x=0 \\ \Leftrightarrow x(8x+12) = 0 \\ \Leftrightarrow x = 0 \vee 8x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{8} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
12. \(-4x^2-16x=0 \\ \Leftrightarrow x(-4x-16) = 0 \\ \Leftrightarrow x = 0 \vee -4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{-4} = -4 \\ V = \Big\{ 0 ; -4 \Big\} \\ -----------------\)