Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2+2x=0\)
2. \(4(-3x^2+3x)=-(20x^2-2x)\)
3. \(-4(7x^2+7x)=-(23x^2+3x)\)
4. \(4(10x^2+10x)=-(-41x^2-49x)\)
5. \(-4x^2-10x=0\)
6. \(15x^2-18x=7x^2-2x\)
7. \(-2x^2-19x=-9x^2-6x\)
8. \(3x^2-1x=0\)
9. \(-6x^2-8x=0\)
10. \(6x^2-19x=2x^2-5x\)
11. \(-4(-6x^2-8x)=-(-17x^2-17x)\)
12. \(5(8x^2+7x)=-(-44x^2-36x)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2+2x=0 \\ \Leftrightarrow x(-x+2) = 0 \\ \Leftrightarrow x = 0 \vee -x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-1} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
2. \(4(-3x^2+3x)=-(20x^2-2x) \\ \Leftrightarrow -12x^2+12x=-20x^2+2x \\ \Leftrightarrow -12x^2+12x+20x^2-2x= 0 \\ \Leftrightarrow 8x^2-10x=0 \\ \Leftrightarrow x(8x-10) = 0 \\ \Leftrightarrow x = 0 \vee 8x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{8} = \frac{5}{4} \\ V = \Big\{ \frac{5}{4}; 0 \Big\} \\ -----------------\)
3. \(-4(7x^2+7x)=-(23x^2+3x) \\ \Leftrightarrow -28x^2-28x=-23x^2-3x \\ \Leftrightarrow -28x^2-28x+23x^2+3x= 0 \\ \Leftrightarrow -5x^2+25x=0 \\ \Leftrightarrow x(-5x+25) = 0 \\ \Leftrightarrow x = 0 \vee -5x+25=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-25}{-5} = 5 \\ V = \Big\{ 5; 0 \Big\} \\ -----------------\)
4. \(4(10x^2+10x)=-(-41x^2-49x) \\ \Leftrightarrow 40x^2+40x=41x^2+49x \\ \Leftrightarrow 40x^2+40x-41x^2-49x= 0 \\ \Leftrightarrow -x^2+9x=0 \\ \Leftrightarrow x(-x+9) = 0 \\ \Leftrightarrow x = 0 \vee -x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-1} = 9 \\ V = \Big\{ 9; 0 \Big\} \\ -----------------\)
5. \(-4x^2-10x=0 \\ \Leftrightarrow x(-4x-10) = 0 \\ \Leftrightarrow x = 0 \vee -4x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-4} = \frac{-5}{2} \\ V = \Big\{ 0 ; \frac{-5}{2} \Big\} \\ -----------------\)
6. \(15x^2-18x=7x^2-2x \\ \Leftrightarrow 8x^2-16x=0 \\ \Leftrightarrow x(8x-16) = 0 \\ \Leftrightarrow x = 0 \vee 8x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{8} = 2 \\ V = \Big\{ 2; 0 \Big\} \\ -----------------\)
7. \(-2x^2-19x=-9x^2-6x \\ \Leftrightarrow 7x^2-13x=0 \\ \Leftrightarrow x(7x-13) = 0 \\ \Leftrightarrow x = 0 \vee 7x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{7} \\ V = \Big\{ \frac{13}{7}; 0 \Big\} \\ -----------------\)
8. \(3x^2-1x=0 \\ \Leftrightarrow x(3x-1) = 0 \\ \Leftrightarrow x = 0 \vee 3x-1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{1}{3} \\ V = \Big\{ \frac{1}{3}; 0 \Big\} \\ -----------------\)
9. \(-6x^2-8x=0 \\ \Leftrightarrow x(-6x-8) = 0 \\ \Leftrightarrow x = 0 \vee -6x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-6} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
10. \(6x^2-19x=2x^2-5x \\ \Leftrightarrow 4x^2-14x=0 \\ \Leftrightarrow x(4x-14) = 0 \\ \Leftrightarrow x = 0 \vee 4x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{4} = \frac{7}{2} \\ V = \Big\{ \frac{7}{2}; 0 \Big\} \\ -----------------\)
11. \(-4(-6x^2-8x)=-(-17x^2-17x) \\ \Leftrightarrow 24x^2+32x=17x^2+17x \\ \Leftrightarrow 24x^2+32x-17x^2-17x= 0 \\ \Leftrightarrow 7x^2-15x=0 \\ \Leftrightarrow x(7x-15) = 0 \\ \Leftrightarrow x = 0 \vee 7x-15=0 \\ \Leftrightarrow x = 0 \vee x = \frac{15}{7} \\ V = \Big\{ \frac{15}{7}; 0 \Big\} \\ -----------------\)
12. \(5(8x^2+7x)=-(-44x^2-36x) \\ \Leftrightarrow 40x^2+35x=44x^2+36x \\ \Leftrightarrow 40x^2+35x-44x^2-36x= 0 \\ \Leftrightarrow -4x^2+1x=0 \\ \Leftrightarrow x(-4x+1) = 0 \\ \Leftrightarrow x = 0 \vee -4x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-4} = \frac{1}{4} \\ V = \Big\{ \frac{1}{4}; 0 \Big\} \\ -----------------\)