Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(3x^2-4x=4x^2+2x\)
2. \(7x^2-26x=2x^2-6x\)
3. \(-2(7x^2-6x)=-(17x^2+5x)\)
4. \(2(-2x^2+4x)=-(8x^2-x)\)
5. \(-5(10x^2-7x)=-(42x^2-16x)\)
6. \(4(-3x^2-10x)=-(5x^2+42x)\)
7. \(-3x^2-7x=-10x^2-10x\)
8. \(-3x^2+13x=0\)
9. \(-3x^2-4x=0\)
10. \(-5(-3x^2+7x)=-(-23x^2+43x)\)
11. \(3(-6x^2-3x)=-(25x^2-4x)\)
12. \(6x^2+24x=7x^2+6x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(3x^2-4x=4x^2+2x \\ \Leftrightarrow -x^2-6x=0 \\ \Leftrightarrow x(-x-6) = 0 \\ \Leftrightarrow x = 0 \vee -x-6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{6}{-1} = -6 \\ V = \Big\{ 0 ; -6 \Big\} \\ -----------------\)
2. \(7x^2-26x=2x^2-6x \\ \Leftrightarrow 5x^2-20x=0 \\ \Leftrightarrow x(5x-20) = 0 \\ \Leftrightarrow x = 0 \vee 5x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{5} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
3. \(-2(7x^2-6x)=-(17x^2+5x) \\ \Leftrightarrow -14x^2+12x=-17x^2-5x \\ \Leftrightarrow -14x^2+12x+17x^2+5x= 0 \\ \Leftrightarrow 3x^2-17x=0 \\ \Leftrightarrow x(3x-17) = 0 \\ \Leftrightarrow x = 0 \vee 3x-17=0 \\ \Leftrightarrow x = 0 \vee x = \frac{17}{3} \\ V = \Big\{ \frac{17}{3}; 0 \Big\} \\ -----------------\)
4. \(2(-2x^2+4x)=-(8x^2-x) \\ \Leftrightarrow -4x^2+8x=-8x^2+x \\ \Leftrightarrow -4x^2+8x+8x^2-x= 0 \\ \Leftrightarrow 4x^2-7x=0 \\ \Leftrightarrow x(4x-7) = 0 \\ \Leftrightarrow x = 0 \vee 4x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{4} \\ V = \Big\{ \frac{7}{4}; 0 \Big\} \\ -----------------\)
5. \(-5(10x^2-7x)=-(42x^2-16x) \\ \Leftrightarrow -50x^2+35x=-42x^2+16x \\ \Leftrightarrow -50x^2+35x+42x^2-16x= 0 \\ \Leftrightarrow -8x^2-19x=0 \\ \Leftrightarrow x(-8x-19) = 0 \\ \Leftrightarrow x = 0 \vee -8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{-8} = \frac{-19}{8} \\ V = \Big\{ 0 ; \frac{-19}{8} \Big\} \\ -----------------\)
6. \(4(-3x^2-10x)=-(5x^2+42x) \\ \Leftrightarrow -12x^2-40x=-5x^2-42x \\ \Leftrightarrow -12x^2-40x+5x^2+42x= 0 \\ \Leftrightarrow -7x^2-2x=0 \\ \Leftrightarrow x(-7x-2) = 0 \\ \Leftrightarrow x = 0 \vee -7x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{-7} = \frac{-2}{7} \\ V = \Big\{ 0 ; \frac{-2}{7} \Big\} \\ -----------------\)
7. \(-3x^2-7x=-10x^2-10x \\ \Leftrightarrow 7x^2+3x=0 \\ \Leftrightarrow x(7x+3) = 0 \\ \Leftrightarrow x = 0 \vee 7x+3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-3}{7} \\ V = \Big\{ 0 ; \frac{-3}{7} \Big\} \\ -----------------\)
8. \(-3x^2+13x=0 \\ \Leftrightarrow x(-3x+13) = 0 \\ \Leftrightarrow x = 0 \vee -3x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{-3} = \frac{13}{3} \\ V = \Big\{ \frac{13}{3}; 0 \Big\} \\ -----------------\)
9. \(-3x^2-4x=0 \\ \Leftrightarrow x(-3x-4) = 0 \\ \Leftrightarrow x = 0 \vee -3x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-3} = \frac{-4}{3} \\ V = \Big\{ 0 ; \frac{-4}{3} \Big\} \\ -----------------\)
10. \(-5(-3x^2+7x)=-(-23x^2+43x) \\ \Leftrightarrow 15x^2-35x=23x^2-43x \\ \Leftrightarrow 15x^2-35x-23x^2+43x= 0 \\ \Leftrightarrow -8x^2-8x=0 \\ \Leftrightarrow x(-8x-8) = 0 \\ \Leftrightarrow x = 0 \vee -8x-8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{8}{-8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
11. \(3(-6x^2-3x)=-(25x^2-4x) \\ \Leftrightarrow -18x^2-9x=-25x^2+4x \\ \Leftrightarrow -18x^2-9x+25x^2-4x= 0 \\ \Leftrightarrow 7x^2+13x=0 \\ \Leftrightarrow x(7x+13) = 0 \\ \Leftrightarrow x = 0 \vee 7x+13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-13}{7} \\ V = \Big\{ 0 ; \frac{-13}{7} \Big\} \\ -----------------\)
12. \(6x^2+24x=7x^2+6x \\ \Leftrightarrow -x^2+18x=0 \\ \Leftrightarrow x(-x+18) = 0 \\ \Leftrightarrow x = 0 \vee -x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-1} = 18 \\ V = \Big\{ 18; 0 \Big\} \\ -----------------\)