Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-17x=9x^2-9x\)
2. \(5(-4x^2-8x)=-(17x^2+63x)\)
3. \(4x^2+19x=0\)
4. \(-6x^2-27x=-7x^2-4x\)
5. \(5x^2+15x=3x^2-5x\)
6. \(-8x^2+20x=0\)
7. \(4(4x^2-6x)=-(-11x^2+26x)\)
8. \(2x^2+1x=0\)
9. \(3(-2x^2-5x)=-(13x^2+17x)\)
10. \(8x^2-11x=0\)
11. \(-5x^2+15x=0\)
12. \(-2(5x^2-5x)=-(17x^2-x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-17x=9x^2-9x \\ \Leftrightarrow -8x^2-8x=0 \\ \Leftrightarrow x(-8x-8) = 0 \\ \Leftrightarrow x = 0 \vee -8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
2. \(5(-4x^2-8x)=-(17x^2+63x) \\ \Leftrightarrow -20x^2-40x=-17x^2-63x \\ \Leftrightarrow -20x^2-40x+17x^2+63x= 0 \\ \Leftrightarrow -3x^2-23x=0 \\ \Leftrightarrow x(-3x-23) = 0 \\ \Leftrightarrow x = 0 \vee -3x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-3} = \frac{-23}{3} \\ V = \Big\{ 0 ; \frac{-23}{3} \Big\} \\ -----------------\)
3. \(4x^2+19x=0 \\ \Leftrightarrow x(4x+19) = 0 \\ \Leftrightarrow x = 0 \vee 4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
4. \(-6x^2-27x=-7x^2-4x \\ \Leftrightarrow x^2-23x=0 \\ \Leftrightarrow x(x-23) = 0 \\ \Leftrightarrow x = 0 \vee x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{1} = 23 \\ V = \Big\{ 23; 0 \Big\} \\ -----------------\)
5. \(5x^2+15x=3x^2-5x \\ \Leftrightarrow 2x^2+20x=0 \\ \Leftrightarrow x(2x+20) = 0 \\ \Leftrightarrow x = 0 \vee 2x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{2} = -10 \\ V = \Big\{ 0 ; -10 \Big\} \\ -----------------\)
6. \(-8x^2+20x=0 \\ \Leftrightarrow x(-8x+20) = 0 \\ \Leftrightarrow x = 0 \vee -8x+20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-20}{-8} = \frac{5}{2} \\ V = \Big\{ \frac{5}{2}; 0 \Big\} \\ -----------------\)
7. \(4(4x^2-6x)=-(-11x^2+26x) \\ \Leftrightarrow 16x^2-24x=11x^2-26x \\ \Leftrightarrow 16x^2-24x-11x^2+26x= 0 \\ \Leftrightarrow 5x^2-2x=0 \\ \Leftrightarrow x(5x-2) = 0 \\ \Leftrightarrow x = 0 \vee 5x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{5} \\ V = \Big\{ \frac{2}{5}; 0 \Big\} \\ -----------------\)
8. \(2x^2+1x=0 \\ \Leftrightarrow x(2x+1) = 0 \\ \Leftrightarrow x = 0 \vee 2x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
9. \(3(-2x^2-5x)=-(13x^2+17x) \\ \Leftrightarrow -6x^2-15x=-13x^2-17x \\ \Leftrightarrow -6x^2-15x+13x^2+17x= 0 \\ \Leftrightarrow 7x^2-2x=0 \\ \Leftrightarrow x(7x-2) = 0 \\ \Leftrightarrow x = 0 \vee 7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{7} \\ V = \Big\{ \frac{2}{7}; 0 \Big\} \\ -----------------\)
10. \(8x^2-11x=0 \\ \Leftrightarrow x(8x-11) = 0 \\ \Leftrightarrow x = 0 \vee 8x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{8} \\ V = \Big\{ \frac{11}{8}; 0 \Big\} \\ -----------------\)
11. \(-5x^2+15x=0 \\ \Leftrightarrow x(-5x+15) = 0 \\ \Leftrightarrow x = 0 \vee -5x+15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-15}{-5} = 3 \\ V = \Big\{ 3; 0 \Big\} \\ -----------------\)
12. \(-2(5x^2-5x)=-(17x^2-x) \\ \Leftrightarrow -10x^2+10x=-17x^2+x \\ \Leftrightarrow -10x^2+10x+17x^2-x= 0 \\ \Leftrightarrow 7x^2-9x=0 \\ \Leftrightarrow x(7x-9) = 0 \\ \Leftrightarrow x = 0 \vee 7x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{7} \\ V = \Big\{ \frac{9}{7}; 0 \Big\} \\ -----------------\)