Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-23x=-3x^2-7x\)
2. \(-6x^2-9x=2x^2+8x\)
3. \(-4(3x^2-8x)=-(17x^2-35x)\)
4. \(2(-9x^2-3x)=-(21x^2-17x)\)
5. \(5(4x^2+10x)=-(-21x^2-57x)\)
6. \(-11x^2+4x=-4x^2+10x\)
7. \(7x^2-1x=0\)
8. \(9x^2-15x=7x^2-10x\)
9. \(-3x^2-1x=0\)
10. \(-6x^2+4x=0\)
11. \(-x^2-3x=0\)
12. \(4x^2-16x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-23x=-3x^2-7x \\ \Leftrightarrow 8x^2-16x=0 \\ \Leftrightarrow x(8x-16) = 0 \\ \Leftrightarrow x = 0 \vee 8x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{8} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
2. \(-6x^2-9x=2x^2+8x \\ \Leftrightarrow -8x^2-17x=0 \\ \Leftrightarrow x(-8x-17) = 0 \\ \Leftrightarrow x = 0 \vee -8x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{-8} = \frac{-17}{8} \\ V = \Big\{ 0 ; \frac{-17}{8} \Big\} \\ -----------------\)
3. \(-4(3x^2-8x)=-(17x^2-35x) \\ \Leftrightarrow -12x^2+32x=-17x^2+35x \\ \Leftrightarrow -12x^2+32x+17x^2-35x= 0 \\ \Leftrightarrow 5x^2+3x=0 \\ \Leftrightarrow x(5x+3) = 0 \\ \Leftrightarrow x = 0 \vee 5x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{5} \\ V = \Big\{ 0 ; \frac{-3}{5} \Big\} \\ -----------------\)
4. \(2(-9x^2-3x)=-(21x^2-17x) \\ \Leftrightarrow -18x^2-6x=-21x^2+17x \\ \Leftrightarrow -18x^2-6x+21x^2-17x= 0 \\ \Leftrightarrow 3x^2+23x=0 \\ \Leftrightarrow x(3x+23) = 0 \\ \Leftrightarrow x = 0 \vee 3x+23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-23}{3} \\ V = \Big\{ 0 ; \frac{-23}{3} \Big\} \\ -----------------\)
5. \(5(4x^2+10x)=-(-21x^2-57x) \\ \Leftrightarrow 20x^2+50x=21x^2+57x \\ \Leftrightarrow 20x^2+50x-21x^2-57x= 0 \\ \Leftrightarrow -x^2+7x=0 \\ \Leftrightarrow x(-x+7) = 0 \\ \Leftrightarrow x = 0 \vee -x+7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-7}{-1} = 7 \\ V = \Big\{ 7; 0 \Big\} \\ -----------------\)
6. \(-11x^2+4x=-4x^2+10x \\ \Leftrightarrow -7x^2-6x=0 \\ \Leftrightarrow x(-7x-6) = 0 \\ \Leftrightarrow x = 0 \vee -7x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-7} = \frac{-6}{7} \\ V = \Big\{ 0 ; \frac{-6}{7} \Big\} \\ -----------------\)
7. \(7x^2-1x=0 \\ \Leftrightarrow x(7x-1) = 0 \\ \Leftrightarrow x = 0 \vee 7x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{7} \\ V = \Big\{ \frac{1}{7}; 0 \Big\} \\ -----------------\)
8. \(9x^2-15x=7x^2-10x \\ \Leftrightarrow 2x^2-5x=0 \\ \Leftrightarrow x(2x-5) = 0 \\ \Leftrightarrow x = 0 \vee 2x-5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
9. \(-3x^2-1x=0 \\ \Leftrightarrow x(-3x-1) = 0 \\ \Leftrightarrow x = 0 \vee -3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{-3} = \frac{-1}{3} \\ V = \Big\{ 0 ; \frac{-1}{3} \Big\} \\ -----------------\)
10. \(-6x^2+4x=0 \\ \Leftrightarrow x(-6x+4) = 0 \\ \Leftrightarrow x = 0 \vee -6x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{-6} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
11. \(-x^2-3x=0 \\ \Leftrightarrow x(-x-3) = 0 \\ \Leftrightarrow x = 0 \vee -x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{-1} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
12. \(4x^2-16x=0 \\ \Leftrightarrow x(4x-16) = 0 \\ \Leftrightarrow x = 0 \vee 4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)