Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-16x=0\)
2. \(-6x^2-2x=0\)
3. \(-2(-6x^2+7x)=-(-11x^2+20x)\)
4. \(-8x^2-11x=0\)
5. \(-2(-10x^2+6x)=-(-24x^2+7x)\)
6. \(3x^2-2x=6x^2-3x\)
7. \(-7x^2-11x=0\)
8. \(-3(2x^2+5x)=-(-2x^2+13x)\)
9. \(-8x^2+11x=0\)
10. \(3x^2-21x=0\)
11. \(5x^2+13x=0\)
12. \(4x^2+11x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-16x=0 \\ \Leftrightarrow x(4x-16) = 0 \\ \Leftrightarrow x = 0 \vee 4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
2. \(-6x^2-2x=0 \\ \Leftrightarrow x(-6x-2) = 0 \\ \Leftrightarrow x = 0 \vee -6x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-6} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
3. \(-2(-6x^2+7x)=-(-11x^2+20x) \\ \Leftrightarrow 12x^2-14x=11x^2-20x \\ \Leftrightarrow 12x^2-14x-11x^2+20x= 0 \\ \Leftrightarrow x^2-6x=0 \\ \Leftrightarrow x(x-6) = 0 \\ \Leftrightarrow x = 0 \vee x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
4. \(-8x^2-11x=0 \\ \Leftrightarrow x(-8x-11) = 0 \\ \Leftrightarrow x = 0 \vee -8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-8} = \frac{-11}{8} \\ V = \Big\{ 0 ; \frac{-11}{8} \Big\} \\ -----------------\)
5. \(-2(-10x^2+6x)=-(-24x^2+7x) \\ \Leftrightarrow 20x^2-12x=24x^2-7x \\ \Leftrightarrow 20x^2-12x-24x^2+7x= 0 \\ \Leftrightarrow -4x^2+5x=0 \\ \Leftrightarrow x(-4x+5) = 0 \\ \Leftrightarrow x = 0 \vee -4x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-4} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
6. \(3x^2-2x=6x^2-3x \\ \Leftrightarrow -3x^2+1x=0 \\ \Leftrightarrow x(-3x+1) = 0 \\ \Leftrightarrow x = 0 \vee -3x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-3} = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
7. \(-7x^2-11x=0 \\ \Leftrightarrow x(-7x-11) = 0 \\ \Leftrightarrow x = 0 \vee -7x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-7} = \frac{-11}{7} \\ V = \Big\{ 0 ; \frac{-11}{7} \Big\} \\ -----------------\)
8. \(-3(2x^2+5x)=-(-2x^2+13x) \\ \Leftrightarrow -6x^2-15x=2x^2-13x \\ \Leftrightarrow -6x^2-15x-2x^2+13x= 0 \\ \Leftrightarrow -8x^2+2x=0 \\ \Leftrightarrow x(-8x+2) = 0 \\ \Leftrightarrow x = 0 \vee -8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
9. \(-8x^2+11x=0 \\ \Leftrightarrow x(-8x+11) = 0 \\ \Leftrightarrow x = 0 \vee -8x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-8} = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
10. \(3x^2-21x=0 \\ \Leftrightarrow x(3x-21) = 0 \\ \Leftrightarrow x = 0 \vee 3x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{3} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
11. \(5x^2+13x=0 \\ \Leftrightarrow x(5x+13) = 0 \\ \Leftrightarrow x = 0 \vee 5x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{5} \\ V = \Big\{ 0 ; \frac{-13}{5} \Big\} \\ -----------------\)
12. \(4x^2+11x=0 \\ \Leftrightarrow x(4x+11) = 0 \\ \Leftrightarrow x = 0 \vee 4x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)