Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(x^2-20x=0\)
2. \(-5(2x^2+3x)=-(6x^2+38x)\)
3. \(8x^2+2x=2x^2-3x\)
4. \(-3x^2+24x=0\)
5. \(-5x^2+x=3x^2-8x\)
6. \(7x^2+24x=0\)
7. \(5(-2x^2+6x)=-(16x^2-20x)\)
8. \(-x^2-24x=-9x^2-5x\)
9. \(2x^2+2x=10x^2+6x\)
10. \(2x^2+15x=-6x^2+7x\)
11. \(-x^2-24x=0\)
12. \(-8x^2-27x=-5x^2-5x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(x^2-20x=0 \\ \Leftrightarrow x(x-20) = 0 \\ \Leftrightarrow x = 0 \vee x-20=0 \\ \Leftrightarrow x = 0 \vee x = \frac{20}{1} = 20 \\ V = \Big\{ 20; 0 \Big\} \\ -----------------\)
2. \(-5(2x^2+3x)=-(6x^2+38x) \\ \Leftrightarrow -10x^2-15x=-6x^2-38x \\ \Leftrightarrow -10x^2-15x+6x^2+38x= 0 \\ \Leftrightarrow -4x^2-23x=0 \\ \Leftrightarrow x(-4x-23) = 0 \\ \Leftrightarrow x = 0 \vee -4x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-4} = \frac{-23}{4} \\ V = \Big\{ 0 ; \frac{-23}{4} \Big\} \\ -----------------\)
3. \(8x^2+2x=2x^2-3x \\ \Leftrightarrow 6x^2+5x=0 \\ \Leftrightarrow x(6x+5) = 0 \\ \Leftrightarrow x = 0 \vee 6x+5=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-5}{6} \\ V = \Big\{ 0 ; \frac{-5}{6} \Big\} \\ -----------------\)
4. \(-3x^2+24x=0 \\ \Leftrightarrow x(-3x+24) = 0 \\ \Leftrightarrow x = 0 \vee -3x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{-3} = 8 \\ V = \Big\{ 8; 0 \Big\} \\ -----------------\)
5. \(-5x^2+x=3x^2-8x \\ \Leftrightarrow -8x^2+9x=0 \\ \Leftrightarrow x(-8x+9) = 0 \\ \Leftrightarrow x = 0 \vee -8x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-8} = \frac{9}{8} \\ V = \Big\{ \frac{9}{8}; 0 \Big\} \\ -----------------\)
6. \(7x^2+24x=0 \\ \Leftrightarrow x(7x+24) = 0 \\ \Leftrightarrow x = 0 \vee 7x+24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-24}{7} \\ V = \Big\{ 0 ; \frac{-24}{7} \Big\} \\ -----------------\)
7. \(5(-2x^2+6x)=-(16x^2-20x) \\ \Leftrightarrow -10x^2+30x=-16x^2+20x \\ \Leftrightarrow -10x^2+30x+16x^2-20x= 0 \\ \Leftrightarrow 6x^2-10x=0 \\ \Leftrightarrow x(6x-10) = 0 \\ \Leftrightarrow x = 0 \vee 6x-10=0 \\ \Leftrightarrow x = 0 \vee x = \frac{10}{6} = \frac{5}{3} \\ V = \Big\{ \frac{5}{3}; 0 \Big\} \\ -----------------\)
8. \(-x^2-24x=-9x^2-5x \\ \Leftrightarrow 8x^2-19x=0 \\ \Leftrightarrow x(8x-19) = 0 \\ \Leftrightarrow x = 0 \vee 8x-19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{19}{8} \\ V = \Big\{ \frac{19}{8}; 0 \Big\} \\ -----------------\)
9. \(2x^2+2x=10x^2+6x \\ \Leftrightarrow -8x^2-4x=0 \\ \Leftrightarrow x(-8x-4) = 0 \\ \Leftrightarrow x = 0 \vee -8x-4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{4}{-8} = \frac{-1}{2} \\ V = \Big\{ 0 ; \frac{-1}{2} \Big\} \\ -----------------\)
10. \(2x^2+15x=-6x^2+7x \\ \Leftrightarrow 8x^2+8x=0 \\ \Leftrightarrow x(8x+8) = 0 \\ \Leftrightarrow x = 0 \vee 8x+8=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-8}{8} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
11. \(-x^2-24x=0 \\ \Leftrightarrow x(-x-24) = 0 \\ \Leftrightarrow x = 0 \vee -x-24=0 \\ \Leftrightarrow x = 0 \vee x = \frac{24}{-1} = -24 \\ V = \Big\{ 0 ; -24 \Big\} \\ -----------------\)
12. \(-8x^2-27x=-5x^2-5x \\ \Leftrightarrow -3x^2-22x=0 \\ \Leftrightarrow x(-3x-22) = 0 \\ \Leftrightarrow x = 0 \vee -3x-22=0 \\ \Leftrightarrow x = 0 \vee x = \frac{22}{-3} = \frac{-22}{3} \\ V = \Big\{ 0 ; \frac{-22}{3} \Big\} \\ -----------------\)