Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+3x=2x^2-3x\)
2. \(5x^2-24x=0\)
3. \(14x^2-6x=9x^2-2x\)
4. \(-8x^2+24x=0\)
5. \(-5(-3x^2+4x)=-(-22x^2+18x)\)
6. \(x^2+5x=5x^2+6x\)
7. \(6x^2-22x=0\)
8. \(-x^2+1x=0\)
9. \(4(-4x^2+9x)=-(24x^2-37x)\)
10. \(x^2+8x=0\)
11. \(5(10x^2-9x)=-(-44x^2+66x)\)
12. \(-8x^2+4x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+3x=2x^2-3x \\ \Leftrightarrow -6x^2+6x=0 \\ \Leftrightarrow x(-6x+6) = 0 \\ \Leftrightarrow x = 0 \vee -6x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-6} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
2. \(5x^2-24x=0 \\ \Leftrightarrow x(5x-24) = 0 \\ \Leftrightarrow x = 0 \vee 5x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{5} \\ V = \Big\{ \frac{24}{5}; 0 \Big\} \\ -----------------\)
3. \(14x^2-6x=9x^2-2x \\ \Leftrightarrow 5x^2-4x=0 \\ \Leftrightarrow x(5x-4) = 0 \\ \Leftrightarrow x = 0 \vee 5x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{5} \\ V = \Big\{ \frac{4}{5}; 0 \Big\} \\ -----------------\)
4. \(-8x^2+24x=0 \\ \Leftrightarrow x(-8x+24) = 0 \\ \Leftrightarrow x = 0 \vee -8x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-8} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
5. \(-5(-3x^2+4x)=-(-22x^2+18x) \\ \Leftrightarrow 15x^2-20x=22x^2-18x \\ \Leftrightarrow 15x^2-20x-22x^2+18x= 0 \\ \Leftrightarrow -7x^2+2x=0 \\ \Leftrightarrow x(-7x+2) = 0 \\ \Leftrightarrow x = 0 \vee -7x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-7} = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)
6. \(x^2+5x=5x^2+6x \\ \Leftrightarrow -4x^2-1x=0 \\ \Leftrightarrow x(-4x-1) = 0 \\ \Leftrightarrow x = 0 \vee -4x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-4} = \frac{-1}{4} \\ V = \Big\{ 0 ; \frac{-1}{4} \Big\} \\ -----------------\)
7. \(6x^2-22x=0 \\ \Leftrightarrow x(6x-22) = 0 \\ \Leftrightarrow x = 0 \vee 6x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{6} = \frac{11}{3} \\ V = \Big\{ \frac{11}{3}; 0 \Big\} \\ -----------------\)
8. \(-x^2+1x=0 \\ \Leftrightarrow x(-x+1) = 0 \\ \Leftrightarrow x = 0 \vee -x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-1} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
9. \(4(-4x^2+9x)=-(24x^2-37x) \\ \Leftrightarrow -16x^2+36x=-24x^2+37x \\ \Leftrightarrow -16x^2+36x+24x^2-37x= 0 \\ \Leftrightarrow 8x^2+1x=0 \\ \Leftrightarrow x(8x+1) = 0 \\ \Leftrightarrow x = 0 \vee 8x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{8} \\ V = \Big\{ 0 ; \frac{-1}{8} \Big\} \\ -----------------\)
10. \(x^2+8x=0 \\ \Leftrightarrow x(x+8) = 0 \\ \Leftrightarrow x = 0 \vee x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{1} = -8 \\ V = \Big\{ 0 ; -8 \Big\} \\ -----------------\)
11. \(5(10x^2-9x)=-(-44x^2+66x) \\ \Leftrightarrow 50x^2-45x=44x^2-66x \\ \Leftrightarrow 50x^2-45x-44x^2+66x= 0 \\ \Leftrightarrow 6x^2-21x=0 \\ \Leftrightarrow x(6x-21) = 0 \\ \Leftrightarrow x = 0 \vee 6x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{6} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
12. \(-8x^2+4x=0 \\ \Leftrightarrow x(-8x+4) = 0 \\ \Leftrightarrow x = 0 \vee -8x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-8} = \frac{1}{2} \\ V = \Big\{ \frac{1}{2}; 0 \Big\} \\ -----------------\)