Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+12x=-5x^2+9x\)
2. \(3x^2-11x=0\)
3. \(17x^2-12x=10x^2+7x\)
4. \(-7x^2+23x=0\)
5. \(6x^2-4x=0\)
6. \(3(-10x^2-8x)=-(23x^2+18x)\)
7. \(-6x^2+13x=0\)
8. \(2x^2+7x=6x^2+6x\)
9. \(7x^2+8x=0\)
10. \(2(-4x^2+7x)=-(15x^2-29x)\)
11. \(2(-9x^2-6x)=-(13x^2+26x)\)
12. \(-11x^2+10x=-7x^2+3x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+12x=-5x^2+9x \\ \Leftrightarrow -x^2+3x=0 \\ \Leftrightarrow x(-x+3) = 0 \\ \Leftrightarrow x = 0 \vee -x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{-1} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
2. \(3x^2-11x=0 \\ \Leftrightarrow x(3x-11) = 0 \\ \Leftrightarrow x = 0 \vee 3x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
3. \(17x^2-12x=10x^2+7x \\ \Leftrightarrow 7x^2-19x=0 \\ \Leftrightarrow x(7x-19) = 0 \\ \Leftrightarrow x = 0 \vee 7x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{7} \\ V = \Big\{ \frac{19}{7}; 0 \Big\} \\ -----------------\)
4. \(-7x^2+23x=0 \\ \Leftrightarrow x(-7x+23) = 0 \\ \Leftrightarrow x = 0 \vee -7x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{-7} = \frac{23}{7} \\ V = \Big\{ \frac{23}{7}; 0 \Big\} \\ -----------------\)
5. \(6x^2-4x=0 \\ \Leftrightarrow x(6x-4) = 0 \\ \Leftrightarrow x = 0 \vee 6x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
6. \(3(-10x^2-8x)=-(23x^2+18x) \\ \Leftrightarrow -30x^2-24x=-23x^2-18x \\ \Leftrightarrow -30x^2-24x+23x^2+18x= 0 \\ \Leftrightarrow -7x^2+6x=0 \\ \Leftrightarrow x(-7x+6) = 0 \\ \Leftrightarrow x = 0 \vee -7x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-7} = \frac{6}{7} \\ V = \Big\{ \frac{6}{7}; 0 \Big\} \\ -----------------\)
7. \(-6x^2+13x=0 \\ \Leftrightarrow x(-6x+13) = 0 \\ \Leftrightarrow x = 0 \vee -6x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-6} = \frac{13}{6} \\ V = \Big\{ \frac{13}{6}; 0 \Big\} \\ -----------------\)
8. \(2x^2+7x=6x^2+6x \\ \Leftrightarrow -4x^2+1x=0 \\ \Leftrightarrow x(-4x+1) = 0 \\ \Leftrightarrow x = 0 \vee -4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-4} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)
9. \(7x^2+8x=0 \\ \Leftrightarrow x(7x+8) = 0 \\ \Leftrightarrow x = 0 \vee 7x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{7} \\ V = \Big\{ 0 ; \frac{-8}{7} \Big\} \\ -----------------\)
10. \(2(-4x^2+7x)=-(15x^2-29x) \\ \Leftrightarrow -8x^2+14x=-15x^2+29x \\ \Leftrightarrow -8x^2+14x+15x^2-29x= 0 \\ \Leftrightarrow 7x^2+15x=0 \\ \Leftrightarrow x(7x+15) = 0 \\ \Leftrightarrow x = 0 \vee 7x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{7} \\ V = \Big\{ 0 ; \frac{-15}{7} \Big\} \\ -----------------\)
11. \(2(-9x^2-6x)=-(13x^2+26x) \\ \Leftrightarrow -18x^2-12x=-13x^2-26x \\ \Leftrightarrow -18x^2-12x+13x^2+26x= 0 \\ \Leftrightarrow -5x^2-14x=0 \\ \Leftrightarrow x(-5x-14) = 0 \\ \Leftrightarrow x = 0 \vee -5x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{-5} = \frac{-14}{5} \\ V = \Big\{ 0 ; \frac{-14}{5} \Big\} \\ -----------------\)
12. \(-11x^2+10x=-7x^2+3x \\ \Leftrightarrow -4x^2+7x=0 \\ \Leftrightarrow x(-4x+7) = 0 \\ \Leftrightarrow x = 0 \vee -4x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-4} = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)