Onvolledige VKV (c=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-6x^2+16x=0\)
2. \(-6x^2-3x=-10x^2-7x\)
3. \(4x^2-21x=0\)
4. \(-2(-8x^2+6x)=-(-15x^2-7x)\)
5. \(6x^2+5x=5x^2+3x\)
6. \(-7x^2+1x=0\)
7. \(6x^2+18x=0\)
8. \(-15x^2-21x=-10x^2+2x\)
9. \(-3x^2-13x=0\)
10. \(5x^2+4x=3x^2+6x\)
11. \(-5x^2+9x=0\)
12. \(4x^2+10x=6x^2-9x\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-6x^2+16x=0 \\ \Leftrightarrow x(-6x+16) = 0 \\ \Leftrightarrow x = 0 \vee -6x+16=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-16}{-6} = \frac{8}{3} \\ V = \Big\{ \frac{8}{3}; 0 \Big\} \\ -----------------\)
2. \(-6x^2-3x=-10x^2-7x \\ \Leftrightarrow 4x^2+4x=0 \\ \Leftrightarrow x(4x+4) = 0 \\ \Leftrightarrow x = 0 \vee 4x+4=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-4}{4} = -1 \\ V = \Big\{ 0 ; -1 \Big\} \\ -----------------\)
3. \(4x^2-21x=0 \\ \Leftrightarrow x(4x-21) = 0 \\ \Leftrightarrow x = 0 \vee 4x-21=0 \\ \Leftrightarrow x = 0 \vee x = \frac{21}{4} \\ V = \Big\{ \frac{21}{4}; 0 \Big\} \\ -----------------\)
4. \(-2(-8x^2+6x)=-(-15x^2-7x) \\ \Leftrightarrow 16x^2-12x=15x^2+7x \\ \Leftrightarrow 16x^2-12x-15x^2-7x= 0 \\ \Leftrightarrow x^2+19x=0 \\ \Leftrightarrow x(x+19) = 0 \\ \Leftrightarrow x = 0 \vee x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{1} = -19 \\ V = \Big\{ 0 ; -19 \Big\} \\ -----------------\)
5. \(6x^2+5x=5x^2+3x \\ \Leftrightarrow x^2+2x=0 \\ \Leftrightarrow x(x+2) = 0 \\ \Leftrightarrow x = 0 \vee x+2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-2}{1} = -2 \\ V = \Big\{ 0 ; -2 \Big\} \\ -----------------\)
6. \(-7x^2+1x=0 \\ \Leftrightarrow x(-7x+1) = 0 \\ \Leftrightarrow x = 0 \vee -7x+1=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-1}{-7} = \frac{1}{7} \\ V = \Big\{ \frac{1}{7}; 0 \Big\} \\ -----------------\)
7. \(6x^2+18x=0 \\ \Leftrightarrow x(6x+18) = 0 \\ \Leftrightarrow x = 0 \vee 6x+18=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-18}{6} = -3 \\ V = \Big\{ 0 ; -3 \Big\} \\ -----------------\)
8. \(-15x^2-21x=-10x^2+2x \\ \Leftrightarrow -5x^2-23x=0 \\ \Leftrightarrow x(-5x-23) = 0 \\ \Leftrightarrow x = 0 \vee -5x-23=0 \\ \Leftrightarrow x = 0 \vee x = \frac{23}{-5} = \frac{-23}{5} \\ V = \Big\{ 0 ; \frac{-23}{5} \Big\} \\ -----------------\)
9. \(-3x^2-13x=0 \\ \Leftrightarrow x(-3x-13) = 0 \\ \Leftrightarrow x = 0 \vee -3x-13=0 \\ \Leftrightarrow x = 0 \vee x = \frac{13}{-3} = \frac{-13}{3} \\ V = \Big\{ 0 ; \frac{-13}{3} \Big\} \\ -----------------\)
10. \(5x^2+4x=3x^2+6x \\ \Leftrightarrow 2x^2-2x=0 \\ \Leftrightarrow x(2x-2) = 0 \\ \Leftrightarrow x = 0 \vee 2x-2=0 \\ \Leftrightarrow x = 0 \vee x = \frac{2}{2} = 1 \\ V = \Big\{ 1; 0 \Big\} \\ -----------------\)
11. \(-5x^2+9x=0 \\ \Leftrightarrow x(-5x+9) = 0 \\ \Leftrightarrow x = 0 \vee -5x+9=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-9}{-5} = \frac{9}{5} \\ V = \Big\{ \frac{9}{5}; 0 \Big\} \\ -----------------\)
12. \(4x^2+10x=6x^2-9x \\ \Leftrightarrow -2x^2+19x=0 \\ \Leftrightarrow x(-2x+19) = 0 \\ \Leftrightarrow x = 0 \vee -2x+19=0 \\ \Leftrightarrow x = 0 \vee x = \frac{-19}{-2} = \frac{19}{2} \\ V = \Big\{ \frac{19}{2}; 0 \Big\} \\ -----------------\)