Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-2x=-3x^2+2x\)
2. \(8x^2+9x=10x^2+6x\)
3. \(-3x^2+14x=0\)
4. \(5x^2-9x=0\)
5. \(-16x^2+26x=-10x^2+4x\)
6. \(9x^2+11x=10x^2+6x\)
7. \(-5x^2+x=2x^2+5x\)
8. \(7x^2-20x=0\)
9. \(14x^2-18x=10x^2+2x\)
10. \(-6x^2-2x=2x^2-4x\)
11. \(-2x^2+20x=-8x^2-3x\)
12. \(8x^2-4x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-2x=-3x^2+2x \\ \Leftrightarrow 4x^2-4x=0 \\ \Leftrightarrow x(4x-4) = 0 \\ \Leftrightarrow x = 0 \vee 4x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{4} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(8x^2+9x=10x^2+6x \\ \Leftrightarrow -2x^2+3x=0 \\ \Leftrightarrow x(-2x+3) = 0 \\ \Leftrightarrow x = 0 \vee -2x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-2} = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
3. \(-3x^2+14x=0 \\ \Leftrightarrow x(-3x+14) = 0 \\ \Leftrightarrow x = 0 \vee -3x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-3} = \frac{14}{3} \\ V = \Big\{ \frac{14}{3}; 0 \Big\} \\ -----------------\)
4. \(5x^2-9x=0 \\ \Leftrightarrow x(5x-9) = 0 \\ \Leftrightarrow x = 0 \vee 5x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
5. \(-16x^2+26x=-10x^2+4x \\ \Leftrightarrow -6x^2+22x=0 \\ \Leftrightarrow x(-6x+22) = 0 \\ \Leftrightarrow x = 0 \vee -6x+22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-22}{-6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
6. \(9x^2+11x=10x^2+6x \\ \Leftrightarrow -x^2+5x=0 \\ \Leftrightarrow x(-x+5) = 0 \\ \Leftrightarrow x = 0 \vee -x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{-1} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
7. \(-5x^2+x=2x^2+5x \\ \Leftrightarrow -7x^2-4x=0 \\ \Leftrightarrow x(-7x-4) = 0 \\ \Leftrightarrow x = 0 \vee -7x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-7} = \frac{-4}{7} \\ V = \Big\{ 0 ; \frac{-4}{7} \Big\} \\ -----------------\)
8. \(7x^2-20x=0 \\ \Leftrightarrow x(7x-20) = 0 \\ \Leftrightarrow x = 0 \vee 7x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{7} \\ V = \Big\{ \frac{20}{7}; 0 \Big\} \\ -----------------\)
9. \(14x^2-18x=10x^2+2x \\ \Leftrightarrow 4x^2-20x=0 \\ \Leftrightarrow x(4x-20) = 0 \\ \Leftrightarrow x = 0 \vee 4x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{4} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
10. \(-6x^2-2x=2x^2-4x \\ \Leftrightarrow -8x^2+2x=0 \\ \Leftrightarrow x(-8x+2) = 0 \\ \Leftrightarrow x = 0 \vee -8x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-8} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
11. \(-2x^2+20x=-8x^2-3x \\ \Leftrightarrow 6x^2+23x=0 \\ \Leftrightarrow x(6x+23) = 0 \\ \Leftrightarrow x = 0 \vee 6x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{6} \\ V = \Big\{ 0 ; \frac{-23}{6} \Big\} \\ -----------------\)
12. \(8x^2-4x=0 \\ \Leftrightarrow x(8x-4) = 0 \\ \Leftrightarrow x = 0 \vee 8x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{8} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)