Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3(5x^2-3x)=-(14x^2-18x)\)
2. \(5x^2-5x=0\)
3. \(8x^2-21x=0\)
4. \(3x^2-15x=0\)
5. \(4x^2+6x=0\)
6. \(-5x^2+14x=0\)
7. \(-8x^2-21x=-7x^2-2x\)
8. \(4x^2+2x=8x^2+7x\)
9. \(5x^2-23x=0\)
10. \(-10x^2-11x=-9x^2-9x\)
11. \(-6x^2-20x=0\)
12. \(11x^2+21x=10x^2+5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3(5x^2-3x)=-(14x^2-18x) \\ \Leftrightarrow -15x^2+9x=-14x^2+18x \\ \Leftrightarrow -15x^2+9x+14x^2-18x= 0 \\ \Leftrightarrow -x^2+9x=0 \\ \Leftrightarrow x(-x+9) = 0 \\ \Leftrightarrow x = 0 \vee -x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
2. \(5x^2-5x=0 \\ \Leftrightarrow x(5x-5) = 0 \\ \Leftrightarrow x = 0 \vee 5x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{5} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
3. \(8x^2-21x=0 \\ \Leftrightarrow x(8x-21) = 0 \\ \Leftrightarrow x = 0 \vee 8x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{8} \\ V = \Big\{ \frac{21}{8}; 0 \Big\} \\ -----------------\)
4. \(3x^2-15x=0 \\ \Leftrightarrow x(3x-15) = 0 \\ \Leftrightarrow x = 0 \vee 3x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{3} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
5. \(4x^2+6x=0 \\ \Leftrightarrow x(4x+6) = 0 \\ \Leftrightarrow x = 0 \vee 4x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{4} = \frac{-3}{2} \\ V = \Big\{ 0 ; \frac{-3}{2} \Big\} \\ -----------------\)
6. \(-5x^2+14x=0 \\ \Leftrightarrow x(-5x+14) = 0 \\ \Leftrightarrow x = 0 \vee -5x+14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-14}{-5} = \frac{14}{5} \\ V = \Big\{ \frac{14}{5}; 0 \Big\} \\ -----------------\)
7. \(-8x^2-21x=-7x^2-2x \\ \Leftrightarrow -x^2-19x=0 \\ \Leftrightarrow x(-x-19) = 0 \\ \Leftrightarrow x = 0 \vee -x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-1} = -19 \\ V = \Big\{ 0 ; -19 \Big\} \\ -----------------\)
8. \(4x^2+2x=8x^2+7x \\ \Leftrightarrow -4x^2-5x=0 \\ \Leftrightarrow x(-4x-5) = 0 \\ \Leftrightarrow x = 0 \vee -4x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{-4} = \frac{-5}{4} \\ V = \Big\{ 0 ; \frac{-5}{4} \Big\} \\ -----------------\)
9. \(5x^2-23x=0 \\ \Leftrightarrow x(5x-23) = 0 \\ \Leftrightarrow x = 0 \vee 5x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{5} \\ V = \Big\{ \frac{23}{5}; 0 \Big\} \\ -----------------\)
10. \(-10x^2-11x=-9x^2-9x \\ \Leftrightarrow -x^2-2x=0 \\ \Leftrightarrow x(-x-2) = 0 \\ \Leftrightarrow x = 0 \vee -x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-1} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
11. \(-6x^2-20x=0 \\ \Leftrightarrow x(-6x-20) = 0 \\ \Leftrightarrow x = 0 \vee -6x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{-6} = \frac{-10}{3} \\ V = \Big\{ 0 ; \frac{-10}{3} \Big\} \\ -----------------\)
12. \(11x^2+21x=10x^2+5x \\ \Leftrightarrow x^2+16x=0 \\ \Leftrightarrow x(x+16) = 0 \\ \Leftrightarrow x = 0 \vee x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{1} = -16 \\ V = \Big\{ 0 ; -16 \Big\} \\ -----------------\)