Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2+8x=-5x^2-10x\)
2. \(4(3x^2+7x)=-(-13x^2-19x)\)
3. \(-5(4x^2+4x)=-(26x^2+27x)\)
4. \(-5x^2-9x=-9x^2+7x\)
5. \(-7x^2+11x=0\)
6. \(-3x^2+2x=-8x^2-10x\)
7. \(2(-7x^2-2x)=-(18x^2-15x)\)
8. \(-3x^2+2x=0\)
9. \(3x^2+0x=0\)
10. \(2x^2-3x=0\)
11. \(2(7x^2+6x)=-(-17x^2-20x)\)
12. \(-4x^2-18x=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2+8x=-5x^2-10x \\ \Leftrightarrow -8x^2+18x=0 \\ \Leftrightarrow x(-8x+18) = 0 \\ \Leftrightarrow x = 0 \vee -8x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{-8} = \frac{9}{4} \\ V = \Big\{ \frac{9}{4}; 0 \Big\} \\ -----------------\)
2. \(4(3x^2+7x)=-(-13x^2-19x) \\ \Leftrightarrow 12x^2+28x=13x^2+19x \\ \Leftrightarrow 12x^2+28x-13x^2-19x= 0 \\ \Leftrightarrow -x^2-9x=0 \\ \Leftrightarrow x(-x-9) = 0 \\ \Leftrightarrow x = 0 \vee -x-9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{9}{-1} = -9 \\ V = \Big\{ 0 ; -9 \Big\} \\ -----------------\)
3. \(-5(4x^2+4x)=-(26x^2+27x) \\ \Leftrightarrow -20x^2-20x=-26x^2-27x \\ \Leftrightarrow -20x^2-20x+26x^2+27x= 0 \\ \Leftrightarrow 6x^2-7x=0 \\ \Leftrightarrow x(6x-7) = 0 \\ \Leftrightarrow x = 0 \vee 6x-7=0 \\ \Leftrightarrow x = 0 \vee x = \frac{7}{6} \\ V = \Big\{ \frac{7}{6}; 0 \Big\} \\ -----------------\)
4. \(-5x^2-9x=-9x^2+7x \\ \Leftrightarrow 4x^2-16x=0 \\ \Leftrightarrow x(4x-16) = 0 \\ \Leftrightarrow x = 0 \vee 4x-16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{16}{4} = 4 \\ V = \Big\{ 4; 0 \Big\} \\ -----------------\)
5. \(-7x^2+11x=0 \\ \Leftrightarrow x(-7x+11) = 0 \\ \Leftrightarrow x = 0 \vee -7x+11=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-11}{-7} = \frac{11}{7} \\ V = \Big\{ \frac{11}{7}; 0 \Big\} \\ -----------------\)
6. \(-3x^2+2x=-8x^2-10x \\ \Leftrightarrow 5x^2+12x=0 \\ \Leftrightarrow x(5x+12) = 0 \\ \Leftrightarrow x = 0 \vee 5x+12=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-12}{5} \\ V = \Big\{ 0 ; \frac{-12}{5} \Big\} \\ -----------------\)
7. \(2(-7x^2-2x)=-(18x^2-15x) \\ \Leftrightarrow -14x^2-4x=-18x^2+15x \\ \Leftrightarrow -14x^2-4x+18x^2-15x= 0 \\ \Leftrightarrow 4x^2+19x=0 \\ \Leftrightarrow x(4x+19) = 0 \\ \Leftrightarrow x = 0 \vee 4x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{4} \\ V = \Big\{ 0 ; \frac{-19}{4} \Big\} \\ -----------------\)
8. \(-3x^2+2x=0 \\ \Leftrightarrow x(-3x+2) = 0 \\ \Leftrightarrow x = 0 \vee -3x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{-3} = \frac{2}{3} \\ V = \Big\{ \frac{2}{3}; 0 \Big\} \\ -----------------\)
9. \(3x^2+0x=0 \\ \Leftrightarrow 3x^2=0 \\ \Leftrightarrow x^2 = \frac{0}{3} \\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(2x^2-3x=0 \\ \Leftrightarrow x(2x-3) = 0 \\ \Leftrightarrow x = 0 \vee 2x-3=0 \\ \Leftrightarrow x = 0 \vee x = \frac{3}{2} \\ V = \Big\{ \frac{3}{2}; 0 \Big\} \\ -----------------\)
11. \(2(7x^2+6x)=-(-17x^2-20x) \\ \Leftrightarrow 14x^2+12x=17x^2+20x \\ \Leftrightarrow 14x^2+12x-17x^2-20x= 0 \\ \Leftrightarrow -3x^2+8x=0 \\ \Leftrightarrow x(-3x+8) = 0 \\ \Leftrightarrow x = 0 \vee -3x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{-3} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
12. \(-4x^2-18x=0 \\ \Leftrightarrow x(-4x-18) = 0 \\ \Leftrightarrow x = 0 \vee -4x-18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{18}{-4} = \frac{-9}{2} \\ V = \Big\{ 0 ; \frac{-9}{2} \Big\} \\ -----------------\)