Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(5x^2+7x)=-(-17x^2+7x)\)
2. \(-4(-3x^2-3x)=-(-7x^2-3x)\)
3. \(-4x^2-11x=0\)
4. \(5(-5x^2-5x)=-(33x^2+14x)\)
5. \(7x^2-16x=0\)
6. \(8x^2+4x=0\)
7. \(6x^2-7x=0\)
8. \(-10x^2-29x=-8x^2-6x\)
9. \(-4(8x^2-7x)=-(38x^2-14x)\)
10. \(-8x^2+0x=0\)
11. \(-11x^2+3x=-10x^2-3x\)
12. \(-10x^2-x=-8x^2+9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(5x^2+7x)=-(-17x^2+7x) \\ \Leftrightarrow 10x^2+14x=17x^2-7x \\ \Leftrightarrow 10x^2+14x-17x^2+7x= 0 \\ \Leftrightarrow -7x^2-21x=0 \\ \Leftrightarrow x(-7x-21) = 0 \\ \Leftrightarrow x = 0 \vee -7x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{-7} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
2. \(-4(-3x^2-3x)=-(-7x^2-3x) \\ \Leftrightarrow 12x^2+12x=7x^2+3x \\ \Leftrightarrow 12x^2+12x-7x^2-3x= 0 \\ \Leftrightarrow 5x^2-9x=0 \\ \Leftrightarrow x(5x-9) = 0 \\ \Leftrightarrow x = 0 \vee 5x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
3. \(-4x^2-11x=0 \\ \Leftrightarrow x(-4x-11) = 0 \\ \Leftrightarrow x = 0 \vee -4x-11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{11}{-4} = \frac{-11}{4} \\ V = \Big\{ 0 ; \frac{-11}{4} \Big\} \\ -----------------\)
4. \(5(-5x^2-5x)=-(33x^2+14x) \\ \Leftrightarrow -25x^2-25x=-33x^2-14x \\ \Leftrightarrow -25x^2-25x+33x^2+14x= 0 \\ \Leftrightarrow 8x^2+11x=0 \\ \Leftrightarrow x(8x+11) = 0 \\ \Leftrightarrow x = 0 \vee 8x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{8} \\ V = \Big\{ 0 ; \frac{-11}{8} \Big\} \\ -----------------\)
5. \(7x^2-16x=0 \\ \Leftrightarrow x(7x-16) = 0 \\ \Leftrightarrow x = 0 \vee 7x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{7} \\ V = \Big\{ \frac{16}{7}; 0 \Big\} \\ -----------------\)
6. \(8x^2+4x=0 \\ \Leftrightarrow x(8x+4) = 0 \\ \Leftrightarrow x = 0 \vee 8x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{8} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
7. \(6x^2-7x=0 \\ \Leftrightarrow x(6x-7) = 0 \\ \Leftrightarrow x = 0 \vee 6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
8. \(-10x^2-29x=-8x^2-6x \\ \Leftrightarrow -2x^2-23x=0 \\ \Leftrightarrow x(-2x-23) = 0 \\ \Leftrightarrow x = 0 \vee -2x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-2} = \frac{-23}{2} \\ V = \Big\{ 0 ; \frac{-23}{2} \Big\} \\ -----------------\)
9. \(-4(8x^2-7x)=-(38x^2-14x) \\ \Leftrightarrow -32x^2+28x=-38x^2+14x \\ \Leftrightarrow -32x^2+28x+38x^2-14x= 0 \\ \Leftrightarrow 6x^2-14x=0 \\ \Leftrightarrow x(6x-14) = 0 \\ \Leftrightarrow x = 0 \vee 6x-14=0 \\ \Leftrightarrow x = 0 \vee x = \frac{14}{6} = \frac{7}{3} \\ V = \Big\{ \frac{7}{3}; 0 \Big\} \\ -----------------\)
10. \(-8x^2+0x=0 \\ \Leftrightarrow -8x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{-8} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-11x^2+3x=-10x^2-3x \\ \Leftrightarrow -x^2+6x=0 \\ \Leftrightarrow x(-x+6) = 0 \\ \Leftrightarrow x = 0 \vee -x+6=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-6}{-1} = 6 \\ V = \Big\{ 6; 0 \Big\} \\ -----------------\)
12. \(-10x^2-x=-8x^2+9x \\ \Leftrightarrow -2x^2-10x=0 \\ \Leftrightarrow x(-2x-10) = 0 \\ \Leftrightarrow x = 0 \vee -2x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{-2} = -5 \\ V = \Big\{ 0 ; -5 \Big\} \\ -----------------\)